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 glm+pn+q. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight glm+pn+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 glm+pn+q-modules arising in this way.