On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
type: Item
instance of: scholarly article
title: On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
zbMATH Open document ID: 0563.14023
DOI: 10.1007/BF01388520
author: Vinay V. Deodhar
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143209
review text: This paper deals with a refinement of the Bruhat cell decomposition for the generalized flag manifold \(G/B\) of a semisimple algebraic group \(G\). It is obtained by intersecting a given Bruhat cell with all cells of the dual decomposition provided by the orbits of the opposite Borel subgroup \(B_-\) on \(G/B\). The intersections decompose themselves as unions of products of affine spaces with tori whose respective dimensions are combinatorially expressed in terms of the Weyl group \(W\) of \(G\). The results can be used to derive explicit formulas for certain polynomials related to the Kazhdan-Lusztig polynomials and to prove the \(L\)-shellability of the Bruhat order on \(W\).
Mathematics Subject Classification ID: 14L40
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 3897117
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Bruhat cell decompositions for generalized flag manifolds
zbMATH Keywords: semisimple algebraic groups
zbMATH Keywords: Kazhdan-Lusztig polynomials
zbMATH Keywords: shellability
MaRDI profile type: Publication
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OpenAlex ID: W2050355762
description: scientific article; zbMATH DE number 3897117