The nil Hecke ring and Deodhar's conjecture on Bruhat intervals
type: Item
instance of: scholarly article
title: The nil Hecke ring and Deodhar's conjecture on Bruhat intervals
zbMATH Open document ID: 0813.20043
DOI: 10.1007/BF01231299
published in: Inventiones Mathematicae
publication date: 1993-06-17T00:00:00Z
full work available at URL: https://eudml.org/doc/144089
review text: The author uses the properties of the ``nil Hecke ring'' proved by \textit{B. Kostant} and \textit{M. Kumar} [Adv. Math. 62, 187-237 (1986; Zbl 0641.17008)] to prove the following: Theorem. Let \((W,R)\) be a Coxeter system and \(\ell : W \to \mathbb{N}\) be the associated length function. Denote the Bruhat order on \(W\) by \(\leq\). Then for any \(v \leq y \leq w\) one has \(\#\{t \in T\mid v\leq ty \leq w\} \geq \ell(w) - \ell(v)\) where \(T\) denotes the set of reflections of \(W\), i.e. the conjugates in \(W\) of the simple reflections.
reviewed by: Ahmed A. Khammash
Mathematics Subject Classification ID: 20F55
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 203555
zbMATH Keywords: nil Hecke ring
zbMATH Keywords: Coxeter system
zbMATH Keywords: length function
zbMATH Keywords: Bruhat order
zbMATH Keywords: reflections
Wikidata QID: Q123201201
author: Matthew Dyer
MaRDI profile type: Publication
cites work: Q4308248
cites work: On the root system of a coxeter group
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cites work: Q4029511
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description: scientific article; zbMATH DE number 203555