The Lusztig isomorphism for Hecke algebras of dihedral type
type: Item
instance of: scholarly article
title: The Lusztig isomorphism for Hecke algebras of dihedral type
zbMATH Open document ID: 0699.20005
DOI: 10.1016/0021-8693(89)90314-1
author: A. P. Fakiolas
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let W denote a finite Coxeter group and H the Hecke algebra of W over \({\mathbb{Q}}(q^{1/2})\), where q is an indeterminate. For W satisfying a certain condition, which holds for Weyl groups, \textit{G. Lusztig} [J. Algebra 71, 490-498 (1981; Zbl 0465.20042)] gave an isomorphism of H to the group algebra of W over \({\mathbb{Q}}(q^{1/2}).\) The author gives explicit formulas for this isomorphism in the case of W being of dihedral type. The author determines the images of the generators of H and of a certain basis of the center of the Hecke algebra H.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 4146229
zbMATH Keywords: finite Coxeter group
zbMATH Keywords: Hecke algebra
zbMATH Keywords: Weyl groups
zbMATH Keywords: group algebra
zbMATH Keywords: dihedral type
zbMATH Keywords: generators
reviewed by: Anton Deitmar
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90314-1
OpenAlex ID: W2000879573
cites work: Q5558293
cites work: Q5580319
cites work: Blocks and Idempotents of Hecke Algebras of General Linear Groups
cites work: Representations of Coxeter groups and Hecke algebras
cites work: On a theorem of Benson and Curtis
description: scientific article; zbMATH DE number 4146229