Infinite-Dimensional Lie Superalgebras and Hook Schur Functions

 Making use of a Howe duality involving the infinite-dimensional Lie superalgebra and the finite-dimensional group GL _l of CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of in terms of hook Schur functions. We use the reduction procedure of to to derive a character formula for a certain class of level 1 highest weight irreducible representations of, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra . These modules turn out to form the complete set of integrable -modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible -modules may be written as a sum of products of hook Schur functions. Received: 6 March 2002 / Accepted: 15 January 2003 Published online: 14 March 2003 RID="*" ID="*" Partially supported by NSC-grant 91-2115-M-002-007 of the R.O.C. RID="**" ID="**" Partially supported by NSC-grant 90-2115-M-006-015 of the R.O.C. Communicated by M. Aizenman