We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition s...We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.展开更多
The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of th...The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o（n ＋ 2, C）. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a^→∈ C^n, we prove that the space forms an irreducible o（n ＋ 2, C）-module for any c ∈ C if a^→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o（n＋2, C） on the polynomial algebra in n variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight o（n ＋2, C）-module with finite-dimensional weight subspaces if c Z/2.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities,NSFC(Grant No.11401559)UCAS(Grant No.Y55202HY00)。
文摘We study inhomogeneous oscillator representations of the strange Lie superalgebras P(n)on supersymmetric polynomial algebras and on spaces of supersymmetric exponential-polynomial functions.We obtain the composition series for these representations.The obtained irreducible modules are infinite dimensional.Some of them are not of highest-weight type and even not weight modules.
基金supported by National Natural Science Foundation of China(Grant Nos.11171324 and 11321101)
文摘The conformal transformations with respect to the metric defining the orthogonal Lie algebra o（n, C） give rise to a one-parameter （c） family of inhomogeneous first-order differential operator representations of the orthogonal Lie algebra o（n ＋ 2, C）. Letting these operators act on the space of exponential-polynomial functions that depend on a parametric vector a^→∈ C^n, we prove that the space forms an irreducible o（n ＋ 2, C）-module for any c ∈ C if a^→ is not on a certain hypersurface. By partially swapping differential operators and multiplication operators, we obtain more general differential operator representations of o（n＋2, C） on the polynomial algebra in n variables. Moreover, we prove that l forms an infinite-dimensional irreducible weight o（n ＋2, C）-module with finite-dimensional weight subspaces if c Z/2.
