The Fock space of m + p bosonic and n + q fermionic quantum oscillators forms a unitarizable module of the general linear superalgebra glm+p n+q. Its tensor powers decompose into direct sums of infinite-dimensional irreducible highest-weight glm+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 glm+p n+q-modules arising in this way.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory