Character and Dimension Formulae for General Linear Superalgebra
نویسنده
چکیده
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. Using the result we establish a one to one correspondence between the set of composition factors of an arbitrary r-fold atypical gl m|n-Kac-module and the set of composition factors of some r-fold atypical gl r|r-Kac-module. The result of Kazhdan-Lusztig polynomials is also applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension of any finite dimensional irreducible representation of the general linear superalgebra.
منابع مشابه
Character and Dimension Formulae for Finite Dimensional Irreducible Representations of the General Linear Superalgebra
The generalized Kazhdan-Lusztig polynomials for the finite dimensional irreducible representations of the general linear superalgebra are computed explicitly. The result is applied to prove a conjectural character formula put forward by van der Jeugt et al in the late 80s. We simplify this character formula to cast it into the Kac-Weyl form, and derive from it a closed formula for the dimension...
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