Infinite-dimensional Lie superalgebras and hook Schur functions

Shun Jen Cheng, Ngau Lam

研究成果: Article同行評審

9 引文 斯高帕斯(Scopus)

摘要

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.

原文English
頁(從 - 到)95-118
頁數24
期刊Communications in Mathematical Physics
238
發行號1-2
DOIs
出版狀態Published - 2003 7月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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