Quasi-finite modules for lie superalgebras of infinite rank

Ngau Lam, R. B. Zhang

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras down curve signgl∞|∞, down curve sign̂ and D̂, and determine the necessary and sufficient conditions for such modules to be unitarizable. The unitarizable irreducible modules are constructed in terms of Fock spaces of free quantum fields, and explicit formulae for their formal characters are also obtained by investigating Howe dualities between the infinite rank Lie superalgebras and classical Lie groups.

Original languageEnglish
Pages (from-to)403-439
Number of pages37
JournalTransactions of the American Mathematical Society
Volume358
Issue number1
DOIs
Publication statusPublished - 2006 Jan 1

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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