Infinite-dimensional Lie Superalgebras and Hook Schur Functions
نویسنده
چکیده
Making use of a Howe duality involving the infinite-dimensional Lie superalgebra ĝl∞|∞ and the finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of ĝl∞|∞ in terms of hook Schur functions. We use the reduction procedure of ĝl∞|∞ to ĝln|n to derive a character formula for a certain class of level 1 highest weight irreducible representations of ĝln|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 ĝln|n-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible ĝlm|n-modules may be written as a sum of products of hook Schur functions.
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