On the new generators of the Hecke algebra \({\mathcal H}(G,U,\mathbf{1})\)
type: Item
instance of: scholarly article
title: On the new generators of the Hecke algebra \({\mathcal H}(G,U,\mathbf{1})\)
zbMATH Open document ID: 0988.20002
author: Jesús Juyumaya
published in: Journal of Algebra
publication date: 1998-11-24T00:00:00Z
review text: The object of this paper is to define Fourier-Grassmann operators for a simple Chevalley group \(G\), and to show that these operators represent the braid group associated to the Weyl group of \(G\). Moreover, they define together with homothetic operators a presentation of a Hecke algebra. In the case where the Cartan matrix of \(G\) is symmetric a construction of a representation module \(\varphi\) of the Weyl group \(W\) of \(G\) is given, and a correspondence in \(\varphi\) between generalized Steinberg representations and certain representations of the semidirect product \(W\ltimes T\), where \(T\) is a maximal torus of a Borel subgroup of \(G\).
reviewed by: Gerhard Burde
Mathematics Subject Classification ID: 20C08
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 1218687
zbMATH Keywords: Fourier-Grassmann operators
zbMATH Keywords: simple Chevalley groups
zbMATH Keywords: braid groups
zbMATH Keywords: Weyl groups
zbMATH Keywords: presentations
zbMATH Keywords: Hecke algebras
zbMATH Keywords: Cartan matrices
zbMATH Keywords: generalized Steinberg representations
zbMATH Keywords: Borel subgroups
MaRDI profile type: Publication
full work available at URL: jabr.1998.7368
OpenAlex ID: W2058754012
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DOI: 10.1006/JABR.1998.7368
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description: scientific article; zbMATH DE number 1218687