James' conjecture for Hecke algebras of exceptional type, I

Meinolf Geck, Juergen Mueller

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper, and a second part to follow, we complete the programme (initiated more than 15 years ago) of determining the decomposition numbers and verifying James' conjecture for Iwahori–Heckealgebras of exceptionaltype. The new ingredients which allow us to achieve this aim are:

•the fact, recently proved by the first author, that all Heckealgebras of finite type are cellular in the sense of Graham–Lehrer, and
•the explicit determination of W-graphs for the irreducible (generic) representations of Heckealgebras of typeE7 and E8 by Howlett and Yin.
Thus, we can reduce the problem of computing decomposition numbers to a manageable size where standard techniques, e.g., Parker's MeatAxe and its variations, can be applied. In this part, we describe the theoretical foundations for this procedure.
Original languageEnglish
Pages (from-to)3274-3298
Number of pages25
JournalJournal of Algebra
Volume321
Issue number11
Early online date5 Dec 2008
DOIs
Publication statusPublished - 1 Jun 2009

Keywords

  • Hecke algebra
  • decomposition numbers
  • James' conjecture

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