Centralizers of Iwahori-Hecke Algebras II: The General Case

Abstract

This paper is a sequel to [4]. We establish the minimal basis theory for the centralizers of parabolic subalgebras of Iwahori-Hecke algebras associated to finite Coxeter groups of any type, generalizing the approach introduced in [3] from centres to the centralizer case. As a pro-requisite, we prove a reducibility property in the twisted J-conjugacy classes in finite Coxeter groups, which is a generalization of results in [7] and [4].

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Correspondence to Andrew Francis.

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2000 Mathematics Subject Classification: 20C08, 20F55

Communicated by Jie Xiao

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Francis, A. Centralizers of Iwahori-Hecke Algebras II: The General Case. Algebra Colloq. 10, 95–100 (2003). https://doi.org/10.1007/s100110300012

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Keywords:

  • Hecke algebra
  • Coxeter group
  • conjugacy class
  • centralizer
  • minimal basis