Making use of a Howe duality involving the infinite-dimensional Lie super-algebra gl∞|∞ and finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of gl∞|∞ in terms of hook Schur functions. We use the reduction procedure of gl∞|∞ to gln|n to derive a character formula for a certain class of level 1 highest weight irreducible representations of gln|n, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra gln|n. These modules turn out to form the complete set of integrable gln|n-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible glm|n-modules may be written as a sum of products of hook Schur functions.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics