In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules i...In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.展开更多
We theoretically investigate the phenomena of electromagnetically induced grating in an M-type five-level atomic system. It is found that a weak field can be effectively diffracted into high-order directions using a s...We theoretically investigate the phenomena of electromagnetically induced grating in an M-type five-level atomic system. It is found that a weak field can be effectively diffracted into high-order directions using a standing wave coupling field, and different depths of the phase modulation can disperse the diffraction light into different orders. When the phase modulation depth is approximated to the orders of π, 2π and 3π, the first-, second- and third-order diffraction intensity reach the maximum, respectively. Thus we can take advantage of the phase modulation to control the probe light dispersing into the required high orders.展开更多
The Lie algebra sl_(2)(C)may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra,so it is natural to consider connections between the representation theory of the two algebras...The Lie algebra sl_(2)(C)may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra,so it is natural to consider connections between the representation theory of the two algebras.In this paper,we explore the restriction to sl_(2)(C)of certain induced modules for the Virasoro algebra.Specifically,we consider Virasoro modules induced from so-called polynomial subalgebras,and we show that the restriction of these modules results in twisted versions of familiar modules such as Verma modules and Whittaker modules.展开更多
In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex represe...In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.展开更多
We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal c...We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.展开更多
Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalge...Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.展开更多
文摘In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11274112 and 11474092the Key Project of Shanghai Municipal Education Commission under Grant No 14ZZ056+1 种基金the Shanghai Natural Science Fund Project under Grant No14ZR1410300the Key Research Project of Henan Province Education Department under Grant No 13A140818
文摘We theoretically investigate the phenomena of electromagnetically induced grating in an M-type five-level atomic system. It is found that a weak field can be effectively diffracted into high-order directions using a standing wave coupling field, and different depths of the phase modulation can disperse the diffraction light into different orders. When the phase modulation depth is approximated to the orders of π, 2π and 3π, the first-, second- and third-order diffraction intensity reach the maximum, respectively. Thus we can take advantage of the phase modulation to control the probe light dispersing into the required high orders.
文摘The Lie algebra sl_(2)(C)may be regarded in a natural way as a subalgebra of the infinite-dimensional Virasoro Lie algebra,so it is natural to consider connections between the representation theory of the two algebras.In this paper,we explore the restriction to sl_(2)(C)of certain induced modules for the Virasoro algebra.Specifically,we consider Virasoro modules induced from so-called polynomial subalgebras,and we show that the restriction of these modules results in twisted versions of familiar modules such as Verma modules and Whittaker modules.
基金supported by National Natural Science Foundation of China (Grant No. 11321101)
文摘In this paper,we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps.In particular,a few classical results of Steinberg and Deligne&Lusztig on complex representations of finite groups of Lie type are extended to reductive algebraic groups with Frobenius maps.
文摘We study the representations of code vertex operator superalgebras resulting from a binary linear code which contains codewords of odd weight. We also show that there exists only one set of seven mutually orthogonal conformal vectors with central charge 1/2 in the Hamming code vertex operator superalgebra MH7. Phrthermore, we classify all the irreducible weak MH7-modules.
文摘Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.
