The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace...The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .展开更多
The author uses the unitary representation theory of SL2(R) to understand the Rankin-Cohen brackets for modular forms. Then this interpretation is used to study the corresponding deformation problems that Paula Cohen,...The author uses the unitary representation theory of SL2(R) to understand the Rankin-Cohen brackets for modular forms. Then this interpretation is used to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.展开更多
For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of uni...For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.展开更多
A rotational parameter Rθ has been introduced to complex wavelet transform （CWT）. The rotational CWT （RCWT） corresponds to a matrix element 〈φ｜U2（θ;μ;κ）[F〉 in the context of quantum mechanics, where U2（...A rotational parameter Rθ has been introduced to complex wavelet transform （CWT）. The rotational CWT （RCWT） corresponds to a matrix element 〈φ｜U2（θ;μ;κ）[F〉 in the context of quantum mechanics, where U2（θ;μ;κ） is a two-mode rotational displacing-squeezing operator in the 〈η｜ representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been proved. The concise proof not only manifestly shows the merit of Dirac＇s representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.展开更多
This study aims to reveal the social representation of fintech from the perspective of traditional financial sector professionals in Brazil—herein used as a proxy for emerging markets—to interpret and compare it wit...This study aims to reveal the social representation of fintech from the perspective of traditional financial sector professionals in Brazil—herein used as a proxy for emerging markets—to interpret and compare it with the scientific literature on the concept of fintech.To achieve this,we applied the social representations theory associated with the word evocation test,similarity analysis,and descending hierarchical classification.After analyzing the results,we perceived a partial misalignment between the existing literature on the concept of fintech and the perspective of traditional financial sector professionals concerning this construct.In contrast to the literature surveyed,the respondents lack perception regarding the potential of fintech to constitute disruptive technology for the traditional financial sector—radically transforming or even eliminating it.In addition,traditional financial sector professionals have little insight into the potential of fintech to financially include the low-income population,owing to their lower costs and greater ease of use.Finally,traditional financial sector professionals failed to appreciate the need to develop a legal and regulatory framework for the performance of fintech in emerging markets.This is a subject that has also been scantly addressed by academia.展开更多
Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical ...Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical skyrmions.The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years,with many photonic microstructures having been devised to this end.Accompanying these designs,scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs.In this work,instead of focusing on a specific type of microstructure,we concentrate on the most common geometric features of these microstructures—namely,symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint.By systematically employing the projection operator technique in group theory,we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette(i.e.,rotational and reflection)symmetries.Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components,such as out-of-plane,radial,azimuthal,and left-and right-handed circular components.Based on these phase singularities,more complicated optical singularities may be synthesized,including C points,V points,L lines,Néel-and bubble-type optical skyrmions,and optical lattices,to name a few.We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure.Lastly,based on symmetry arguments,we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity.Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries,shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.展开更多
Drawing on Social Representation Theory,this study analyzes an authentic corpus from Sina Weibo during the Tokyo Olympics,focusing on textual visual,and performative symbols embedded in Olympic-themed microblogs and t...Drawing on Social Representation Theory,this study analyzes an authentic corpus from Sina Weibo during the Tokyo Olympics,focusing on textual visual,and performative symbols embedded in Olympic-themed microblogs and their comment sections.It investigates the interactive mechanisms through which national identity is constructed within the digital media environment,emphasizing the processes of symbol generation,reception,and reproduction.The findings reveal that these symbolic elements disseminate national imagery through the dual processes of anchoring and objectification,producing a top-down emotional and visual resonance.Meanwhile,the repetitive imitation and creative recontextualization of various symbols by individuals in Weibo comment sections demonstrate how national identity is not only accepted but also continuously reproduced through interactive practices,revealing a bottom-up co-creation dynamic.This study addresses the oversight of individual agency in macro-discourse approaches,revealing the reciprocal pathways of national identity construction in digital spaces and offering novel theoretical perspectives for researching national identity in the digital era.展开更多
The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representatio...The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.展开更多
A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss...A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss in size. Numerical results are given for both the original problem and the reduced problem to make a comparison.展开更多
In the treatment of diseases or illnesses,modern medicine is used as well as traditional medicine practices.Medicinal plants are commonly used in traditional medicine.For this reason,it is seen in the literature that ...In the treatment of diseases or illnesses,modern medicine is used as well as traditional medicine practices.Medicinal plants are commonly used in traditional medicine.For this reason,it is seen in the literature that this subject is generally studied from pharmacology or ethnobotanical perspective.However,in-home practices,it is seen that gastronomic products are also used for healing purposes,along with medicinal and aromatic plants.This research is conducted in order to identify the remedial use of food/beverages and to evaluate them within the scope of social representation theory.The qualitative research method was preferred as the best way to observe social representations and semi-structured interviews were conducted with 20 people.As a result of the interviews,it was determined that 107 different practices were applied in the treatment of 35 diseases.These practices have been evaluated in the context of social representations,and it was concluded that scientific knowledge and common-sense.展开更多
Recently an f -deformed Fock space which is spanned by ｜ n λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new nonorthogonal basis ...Recently an f -deformed Fock space which is spanned by ｜ n λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by ｜ n λ bases, to a new one, spanned by extended two-parameters bases ｜ n λ 1 ,λ 2 . These bases are now the eigenstates of a non-Hermitian Hamiltonian H λ 1 ,λ 2 = a λ 1 ,λ 2 a ＋ 1 2 , where a λ 1 ,λ 2 = a ＋ λ 1 a ＋ λ 2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases ｜ n λ 1 ,λ 2 are nonorthogonal （squeezed states）, but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.展开更多
We discuss the role of diflterential equations in Lie group representation theory.We use Kashiwara's pentagon as a reference frame for the real representation theory and then report on some work arising from its p...We discuss the role of diflterential equations in Lie group representation theory.We use Kashiwara's pentagon as a reference frame for the real representation theory and then report on some work arising from its p-adic analogue by Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch using Berthelofs theory of arithmetic D-modules and Schneider-Stuhler theory of sheaves on buildings.展开更多
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory.The author reviews some main convergence results,conjectures and problems in the co...Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory.The author reviews some main convergence results,conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras.He also reviews the related analytic extension results,conjectures and problems.He discusses the convergence and analytic extensions of products of intertwining operators(chiral conformal fields)and of q-traces and pseudo-q-traces of products of intertwining operators.He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result.He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.展开更多
This essay treats the understanding of poetry, especially lyric poetry, as representation. The theme is developed partly as a historical survey, from the Classical Age to Romanticism and to Modernism, and through the ...This essay treats the understanding of poetry, especially lyric poetry, as representation. The theme is developed partly as a historical survey, from the Classical Age to Romanticism and to Modernism, and through the history of aesthetics in Western terms. It offers critical scrutiny with the intention to explore a more justifiable theory of representation. Hopefully it may help to understand lyric poetry in historical contexts from Plato and Aristotle＇s imitation theories, to Beardsley＇s theory of illocutionary action and New Criticism. It is the image in lyric poetry that accounts for human action＇s being represented. Poetic beauty is an illusionary reality, as that in painting, and the role of image has been widely appreciated in producing this beauty as verbal icon. Finally, I mention the connection between Western theorizing of poetry as representation and Chinese poetry and poetics in general. We see the possibility that the importance of lyric poetry as representation can encourage comparative literature and world literature, and a general theory of representation. These might be informative in Chinese literary studies, from a theoretical point of view.展开更多
This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl2（C）. We then c...We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl2（C）. We then consider the free Lie algebra on three generators, and compute the Lie invariants of degree ≤ 7 corresponding to the adjoint representation of sl2（C）, and the Lie invariants of degree ≤ 9 corresponding to the natural representation of sl3（C）. We represent the action of sl2（C） and sl3（C） on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words.展开更多
The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ...The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.展开更多
We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.
In this paper, we give the eigenvalues of the manifold Sp（n）/U（n）. We prove that an eigenvalue λs（f1,f2,...,fn） of the Lie group Sp（n）, corresponding to the representation with label （f1, f2,..., fn）, is an...In this paper, we give the eigenvalues of the manifold Sp（n）/U（n）. We prove that an eigenvalue λs（f1,f2,...,fn） of the Lie group Sp（n）, corresponding to the representation with label （f1, f2,..., fn）, is an eigenvalue of the manifold Sp（n）/U（n）, if and only if f1, f2,..., fn are all even.展开更多
文摘The relation between the normal displacement on the surface of a dynamical elliptical crack and the normal stress over the crack surface was studied. The three dimensional elastodynamic equations and Fourier Laplace transforms are used. Based on the influence function and the inversion of integral transforms, one can find that if the distribution of normal displacement on the surface of a dynamic elliptical crack is a polynomial of degree n in x 1 and x 2 , then the normal pressure acting over the ellipse is also a polynomial P n(x 1,x 2) of the same degree in x 1 and x 2 .
基金supported by the National Natural Science Foundation of China(No.11231002)
文摘The author uses the unitary representation theory of SL2(R) to understand the Rankin-Cohen brackets for modular forms. Then this interpretation is used to study the corresponding deformation problems that Paula Cohen, Yuri Manin and Don Zagier initiated. Two uniqueness results are established.
文摘For a special use a new modelling method of evaluating external disturbing potential is presented in this paper.Being different from classical methods in physical geodesy this method is grounded upon the theory of unified representation of gravitational field.The models created in this way are particularly satisfactory for a high_speed computation of gravitational field in low altitude because they take account of topographic effects and have their kernel functions with simple structure and weak singularity.
基金National Natural Science Foundation of China under Grant No.10647133the Research Foundation of the Education Department of Jiangxi Province under Grant No.[2007]22
文摘A rotational parameter Rθ has been introduced to complex wavelet transform （CWT）. The rotational CWT （RCWT） corresponds to a matrix element 〈φ｜U2（θ;μ;κ）[F〉 in the context of quantum mechanics, where U2（θ;μ;κ） is a two-mode rotational displacing-squeezing operator in the 〈η｜ representation. Based on this, the Parseval theorem and the inversion formula of RCWT have been proved. The concise proof not only manifestly shows the merit of Dirac＇s representation theory but also leads to a new orthogonal property of complex mother wavelets in parameter space.
基金supported by the Brazilian National Council for Scientific and Technological Development(CNPq)under the grant number 306517/2018–3(LAJ)and Brazilian School of Public and Business Administration at Getulio Vargas Foundation under grant number Propesquisa 00505100300360(LAJ).
文摘This study aims to reveal the social representation of fintech from the perspective of traditional financial sector professionals in Brazil—herein used as a proxy for emerging markets—to interpret and compare it with the scientific literature on the concept of fintech.To achieve this,we applied the social representations theory associated with the word evocation test,similarity analysis,and descending hierarchical classification.After analyzing the results,we perceived a partial misalignment between the existing literature on the concept of fintech and the perspective of traditional financial sector professionals concerning this construct.In contrast to the literature surveyed,the respondents lack perception regarding the potential of fintech to constitute disruptive technology for the traditional financial sector—radically transforming or even eliminating it.In addition,traditional financial sector professionals have little insight into the potential of fintech to financially include the low-income population,owing to their lower costs and greater ease of use.Finally,traditional financial sector professionals failed to appreciate the need to develop a legal and regulatory framework for the performance of fintech in emerging markets.This is a subject that has also been scantly addressed by academia.
基金supported by the National Natural Science Foun-dation of China(62301596 and 62288101)Shaanxi Provincial Science and Technology Innovation Team(23-CX-TD-48)+4 种基金the KU Leuven internal funds:the C1 Project(C14/19/083)the Interdisciplinary Network Project(IDN/20/014)the Small Infrastructure Grant(KA/20/019)the Research Foundation of Flanders(FWO)Project(G090017N,G088822N,and V408823N)the Danish National Research Foundation(DNRF165).
文摘Optical singularities are topological defects of electromagnetic fields;they include phase singularity in scalar fields,polarization singularity in vector fields,and three-dimensional(3D)singularities such as optical skyrmions.The exploitation of photonic microstructures to generate and manipulate optical singularities has attracted wide research interest in recent years,with many photonic microstructures having been devised to this end.Accompanying these designs,scattered phenomenological theories have been proposed to expound the working mechanisms behind individual designs.In this work,instead of focusing on a specific type of microstructure,we concentrate on the most common geometric features of these microstructures—namely,symmetries—and revisit the process of generating optical singularities in microstructures from a symmetry viewpoint.By systematically employing the projection operator technique in group theory,we develop a widely applicable theoretical scheme to explore optical singularities in microstructures with rosette(i.e.,rotational and reflection)symmetries.Our scheme agrees well with previously reported works and further reveals that the eigenmodes of a symmetric microstructure can support multiplexed phase singularities in different components,such as out-of-plane,radial,azimuthal,and left-and right-handed circular components.Based on these phase singularities,more complicated optical singularities may be synthesized,including C points,V points,L lines,Néel-and bubble-type optical skyrmions,and optical lattices,to name a few.We demonstrate that the topological invariants associated with optical singularities are protected by the symmetries of the microstructure.Lastly,based on symmetry arguments,we formulate a so-called symmetry matching condition to clarify the excitation of a specific type of optical singularity.Our work establishes a unified theoretical framework to explore optical singularities in photonic microstructures with symmetries,shedding light on the symmetry origin of multidimensional and multiplexed optical singularities and providing a symmetry perspective for exploring many singularity-related effects in optics and photonics.
文摘Drawing on Social Representation Theory,this study analyzes an authentic corpus from Sina Weibo during the Tokyo Olympics,focusing on textual visual,and performative symbols embedded in Olympic-themed microblogs and their comment sections.It investigates the interactive mechanisms through which national identity is constructed within the digital media environment,emphasizing the processes of symbol generation,reception,and reproduction.The findings reveal that these symbolic elements disseminate national imagery through the dual processes of anchoring and objectification,producing a top-down emotional and visual resonance.Meanwhile,the repetitive imitation and creative recontextualization of various symbols by individuals in Weibo comment sections demonstrate how national identity is not only accepted but also continuously reproduced through interactive practices,revealing a bottom-up co-creation dynamic.This study addresses the oversight of individual agency in macro-discourse approaches,revealing the reciprocal pathways of national identity construction in digital spaces and offering novel theoretical perspectives for researching national identity in the digital era.
文摘The draping behavior of fabric is simulated by using four node quadrilateral thin plate elements with finite rotation. The finite element formulation is based on the total Lagrangian approach. An exact representation of finite rotation is introduced. The strain energy function accounting for the material symmetry is obtained by the tensor representation theory. To avoid shear locking, the assumed strain technique for transverse shear is adopted. The conjugate gradient method with a proposed line search algorithm is employed to minimize energy and reach the final shape of fabric. The draping behavior of a rectangular piece of fabric over a rectangular table is simulated. (Author abstract) 9 Refs.
基金Project supported by the National Natural Science Foundation of China (Grant No.10771133)the Research Fundation for the Doctoral Program of Higher Education (Grant No.200802800010)the Key Disciplines of Shanghai Municipality (GrantNo.s30104)
文摘A reduction of truss topology design problem formulated by semidefinite optimization （SDO） is considered. The finite groups and their representations are introduced to reduce the stiffness and mass matrices of truss in size. Numerical results are given for both the original problem and the reduced problem to make a comparison.
文摘In the treatment of diseases or illnesses,modern medicine is used as well as traditional medicine practices.Medicinal plants are commonly used in traditional medicine.For this reason,it is seen in the literature that this subject is generally studied from pharmacology or ethnobotanical perspective.However,in-home practices,it is seen that gastronomic products are also used for healing purposes,along with medicinal and aromatic plants.This research is conducted in order to identify the remedial use of food/beverages and to evaluate them within the scope of social representation theory.The qualitative research method was preferred as the best way to observe social representations and semi-structured interviews were conducted with 20 people.As a result of the interviews,it was determined that 107 different practices were applied in the treatment of 35 diseases.These practices have been evaluated in the context of social representations,and it was concluded that scientific knowledge and common-sense.
文摘Recently an f -deformed Fock space which is spanned by ｜ n λ was introduced. These bases are the eigenstates of a deformed non-Hermitian Hamiltonian. In this contribution, we will use rather new nonorthogonal basis vectors for the construction of coherent and squeezed states, which in special case lead to the earlier known states. For this purpose, we first generalize the previously introduced Fock space spanned by ｜ n λ bases, to a new one, spanned by extended two-parameters bases ｜ n λ 1 ,λ 2 . These bases are now the eigenstates of a non-Hermitian Hamiltonian H λ 1 ,λ 2 = a λ 1 ,λ 2 a ＋ 1 2 , where a λ 1 ,λ 2 = a ＋ λ 1 a ＋ λ 2 and a are, respectively, the deformed creation and ordinary bosonic annihilation operators. The bases ｜ n λ 1 ,λ 2 are nonorthogonal （squeezed states）, but normalizable. Then, we deduce the new representations of coherent and squeezed states in our two-parameter Fock space. Finally, we discuss the quantum statistical properties, as well as the non-classical properties of the obtained states numerically.
文摘We discuss the role of diflterential equations in Lie group representation theory.We use Kashiwara's pentagon as a reference frame for the real representation theory and then report on some work arising from its p-adic analogue by Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch using Berthelofs theory of arithmetic D-modules and Schneider-Stuhler theory of sheaves on buildings.
文摘Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory.The author reviews some main convergence results,conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras.He also reviews the related analytic extension results,conjectures and problems.He discusses the convergence and analytic extensions of products of intertwining operators(chiral conformal fields)and of q-traces and pseudo-q-traces of products of intertwining operators.He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result.He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.
文摘This essay treats the understanding of poetry, especially lyric poetry, as representation. The theme is developed partly as a historical survey, from the Classical Age to Romanticism and to Modernism, and through the history of aesthetics in Western terms. It offers critical scrutiny with the intention to explore a more justifiable theory of representation. Hopefully it may help to understand lyric poetry in historical contexts from Plato and Aristotle＇s imitation theories, to Beardsley＇s theory of illocutionary action and New Criticism. It is the image in lyric poetry that accounts for human action＇s being represented. Poetic beauty is an illusionary reality, as that in painting, and the role of image has been widely appreciated in producing this beauty as verbal icon. Finally, I mention the connection between Western theorizing of poetry as representation and Chinese poetry and poetics in general. We see the possibility that the importance of lyric poetry as representation can encourage comparative literature and world literature, and a general theory of representation. These might be informative in Chinese literary studies, from a theoretical point of view.
文摘This paper proves that the restriction of a Specht module for a(degenerate or non-degenerate)cyclotomic Hecke algebra, or KLR(Khovanov-Lauda-Rouquier) algebra, of type A has a Specht filtration.
文摘We use computer algebra to determine the Lie invariants of degree ≤ 12 in the free Lie algebra on two generators corresponding to the natural representation of the simple 3-dimensional Lie algebra sl2（C）. We then consider the free Lie algebra on three generators, and compute the Lie invariants of degree ≤ 7 corresponding to the adjoint representation of sl2（C）, and the Lie invariants of degree ≤ 9 corresponding to the natural representation of sl3（C）. We represent the action of sl2（C） and sl3（C） on Lie polynomials by computing the coefficient matrix with respect to the basis of Hall words.
文摘The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.
文摘We give an introduction to basic harmonic analysis and representation theory for homogeneous spaces Z = G/H attached to a real reductive Lie group G. A special emphasis is made to the case where Z is real spherical.
文摘In this paper, we give the eigenvalues of the manifold Sp（n）/U（n）. We prove that an eigenvalue λs（f1,f2,...,fn） of the Lie group Sp（n）, corresponding to the representation with label （f1, f2,..., fn）, is an eigenvalue of the manifold Sp（n）/U（n）, if and only if f1, f2,..., fn are all even.
