Infinite-dimensional Lie superalgebras and hook Schur functions

Shun Jen Cheng, Ngau Lam

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)95-118
Number of pages24
JournalCommunications in Mathematical Physics
Volume238
Issue number1-2
DOIs
Publication statusPublished - 2003 Jan 1

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Schur Functions
hooks
Lie Superalgebra
Character Formula
modules
Module
Irreducible Representation
Duality
algebra
products
Class

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

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Infinite-dimensional Lie superalgebras and hook Schur functions. / Cheng, Shun Jen; Lam, Ngau.

In: Communications in Mathematical Physics, Vol. 238, No. 1-2, 01.01.2003, p. 95-118.

Research output: Contribution to journalArticle

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