Comparison of the Bruhat and the Iwahori decompositions of a \(p\)-adic Chevalley group
type: Item
instance of: scholarly article
title: Comparison of the Bruhat and the Iwahori decompositions of a \(p\)-adic Chevalley group
zbMATH Open document ID: 0836.22014
author: V. Pereyra
published in: Journal of Algebra
publication date: 1994-10-12T00:00:00Z
review text: Let \(G\) be a \(p\)-adic Chevalley group. The decomposition of \(G\) into double cosets under a Borel subgroup, the Bruhat decomposition, is indexed by the small Weyl group of \(G\). An Iwahori subgroup, i.e. the inverse image of a Borel subgroup of the finite quotient, gives a double coset decomposition indexed by the big Weyl group. In the paper the author introduces an ``integer structure'' on the Bruhat cells to get a refined decomposition, again indexed by the big Weyl group. A comparison theorem then gives a criterion in terms of the Weyl group to decide when two cells of the two types have a nonvoid intersection.
reviewed by: Anton Deitmar
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 638513
zbMATH Keywords: \(p\)-adic Chevalley group
zbMATH Keywords: Borel subgroup
zbMATH Keywords: Bruhat decomposition
zbMATH Keywords: Weyl group
zbMATH Keywords: Iwahori subgroup
zbMATH Keywords: Bruhat cells
MaRDI profile type: Publication
full work available at URL: jabr.1994.1208
OpenAlex ID: W2055355510
DOI: 10.1006/JABR.1994.1208
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description: scientific article; zbMATH DE number 638513