Upper and lower bounds for Kazhdan-Lusztig polynomials
type: Item
instance of: scholarly article
title: Upper and lower bounds for Kazhdan-Lusztig polynomials
zbMATH Open document ID: 0904.20035
author: Francesco Brenti
published in: European Journal of Combinatorics
publication date: 1999-01-20T00:00:00Z
review text: The author gives upper and lower bounds for the Kazhdan-Lusztig polynomials of any Coxeter group \(W\) and shows that if \(W\) is finite then the \(k\)th coefficient of the Kazhdan-Lusztig polynomial of two elements \(u\), \(v\) of \(W\) is bounded from above by a polynomial (which depends only on \(k\)) in \(l(v)-l(u)\) for any \(k\geq 0\). This implies the validity of Lascoux-Schützenberger's conjecture for all sufficiently long intervals and gives supporting evidence in favour of the Dyer-Lusztig conjecture.
reviewed by: Chiu Sen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 05E15
Mathematics Subject Classification ID: 20F55
zbMATH DE Number: 1199950
zbMATH Keywords: Bruhat order
zbMATH Keywords: Kazhdan-Lusztig polynomials
zbMATH Keywords: Coxeter groups
zbMATH Keywords: Lascoux-Schützenberger conjecture
zbMATH Keywords: Dyer-Lusztig conjecture
MaRDI profile type: Publication
full work available at URL: eujc.1997.0178
OpenAlex ID: W2017558223
DOI: 10.1006/EUJC.1997.0178
description: scientific article; zbMATH DE number 1199950