Abstract
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.
Original language | English |
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Pages (from-to) | 95-118 |
Number of pages | 24 |
Journal | Communications in Mathematical Physics |
Volume | 238 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 2003 Jul |
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics