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

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