Modular representation theory over a ring of higher dimension with applications to Hecke algebras
type: Item
instance of: scholarly article
title: Modular representation theory over a ring of higher dimension with applications to Hecke algebras
zbMATH Open document ID: 0833.20054
author: Akihiko Gyoja
published in: Journal of Algebra
publication date: 1995-08-29T00:00:00Z
review text: Let \((W,S)\) be a Coxeter system, \(r = (r_s)_{s\in S}\) a system of indeterminates such that \(r_s = r_{s'}\) if and only if \(s\) and \(s'\) are \(W\)-conjugate and different \(r_s\)'s are algebraically independent, \(R = \mathbb{Z}[r]\), and \(H(R)\) a free \(R\)-module with a basis \(\{T_W\}_{w \in W}\). Let \(F\) be a field, \(O : R \to F\) a ring homomorphism, and assume \(W\) finite. The author shows that \(H(R) \otimes F\) is semisimple if and only if the specialization by \(O\) of every generic degree divided by the Poincaré polynomial is well-defined.
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 20C30
zbMATH DE Number: 783876
zbMATH Keywords: Hecke algebra
zbMATH Keywords: Coxeter system
zbMATH Keywords: Poincaré polynomial
reviewed by: Chiu Sen
MaRDI profile type: Publication
full work available at URL: jabr.1995.1139
OpenAlex ID: W2002693619
DOI: 10.1006/JABR.1995.1139
description: scientific article; zbMATH DE number 783876