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

Abstract

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

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References in corpus (1)

• Spinor Algebras

Cited by in corpus (1)

• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams