## Abstract

Making use of a Howe duality involving the infinite-dimensional Lie super-algebra gl_{∞|∞} and finite-dimensional group GL_{l} 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 gl_{n|n} to derive a character formula for a certain class of level 1 highest weight irreducible representations of gl_{n|n}, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra gl_{n|n}. These modules turn out to form the complete set of integrable gl_{n|n}-modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible gl_{m|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