The weighted fusion category algebra and the q-Schur algebra for GL(2)(q)

Sejong Park

Research output: Contribution to journalArticle

Abstract

We show that the weighted fusion category algebra of the principal 2-block b(0) of GL(2)(q) is the quotient of the q-Schur algebra S-2(q) by its socle, for q an odd prime power. As a consequence, we get a canonical bijection between the set of isomorphism classes of simple kGL(2) (q)b(0)-modules and the set of conjugacy classes of b(0)-weights in this case. (C) 2007 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)93-101
Number of pages9
JournalJournal of Algebra
Volume319
Issue number1
DOIs
Publication statusPublished - 1 Jan 2008

Keywords

  • function system
  • weighted fusion category algebra
  • Alperin's weight conjecture
  • q-Schur algebra
  • general linear-groups

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