Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra

Details Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra Character Formula for Infinite Dimensional Unitarizable Modules of the General Linear Superalgebra

2003-01-17

arxiv.org/abs/math/0301183v1

Journal of Algebra 273 (2004) 780-805

Mathematics

Representation Theory

25 Pages, LaTeX format

Scientific paper

The Fock space of $m+p$ bosonic and $n+q$ fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra $gl_{m+p|n+q}$. Its tensor powers decompose into direct sums of infinite dimensional irreducible highest weight $gl_{m+p|n+q}$-modules. We obtain an explicit decomposition of any tensor power of this Fock space into irreducibles, and develop a character formula for the irreducible $gl_{m+p|n+q}$-modules arising in this way.

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