Inducing \(W\)-graphs.
type: Item
instance of: scholarly article
title: Inducing \(W\)-graphs.
zbMATH Open document ID: 1045.20005
author: R. B. Howlett
author: Yunchuan Yin
published in: Mathematische Zeitschrift
publication date: 2003-08-17T00:00:00Z
review text: Let \(W=(W,S)\) be a Coxeter group with \(S\) the set of simple reflections. Let \(\mathcal H\) be the corresponding Hecke algebra over the ring \(\mathcal A=\mathbb{Z}[q^{-1/2},q^{1/2}]\). \textit{D. Kazhdan} and \textit{G. Lusztig} defined a \(W\)-graph [Invent. Math. 53, 165-184 (1979; Zbl 0499.20035)] which provides a representation of the algebra \(\mathcal H\). In the paper under review, the authors show that if \(W_J\) is a standard parabolic subgroup of \(W\) and \(V\) is a module for the corresponding Hecke algebra \({\mathcal H}_J\), then a \(W_J\)-graph structure for \(V\) gives rise to a \(W\)-graph structure for the induced module \({\mathcal H}\otimes_{{\mathcal H}_J}V\). In the case that \(J=\emptyset\) and \(V\) has dimension 1, the construction given in the paper coincides with that by Kazhdan and Lusztig for the regular representation of \(\mathcal H\). For an arbitrary \(J\) and one-dimensional \(V\), the paper recovers the constructions by \textit{M. Couillens} [J. Algebra 213, No. 2, 687-720 (1999; Zbl 0981.20031)] and \textit{V. Deodhar} [J. Algebra 190, No. 1, 214-225 (1997; Zbl 0889.20021)].
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 1965497
zbMATH Keywords: \(W\)-graphs
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Hecke algebras
MaRDI profile type: Publication
full work available at URL: s00209-003-0507-1
OpenAlex ID: W44173902
DOI: 10.1007/S00209-003-0507-1
description: scientific article; zbMATH DE number 1965497