Stratifying endomorphism algebras associated to Hecke algebras
type: Item
instance of: scholarly article
title: Stratifying endomorphism algebras associated to Hecke algebras
zbMATH Open document ID: 0920.20008
author: Jie Du
author: Brian J. Parshall
author: Leonard L. Scott
published in: Journal of Algebra
publication date: 1999-09-20T00:00:00Z
review text: Let \(G\) be a finite group of Lie type and let \(k\) be a field of characteristic distinct from the defining characteristic of \(G\). This paper presents a systematic study of the structure and homological algebra for the endomorphism algebra \(S(G,k)=\text{End}_{kG}\bigl(\bigoplus_J\text{Ind}^G_{P_J}k\bigr)\). The structure of this algebra turns out to involve new applications of Kazhdan-Lusztig cell theory. Two stratification conjectures made by \textit{E. Chine}, \textit{B. Parshall} and \textit{L. Scott} [Mem. Am. Math. Soc. 591 (1996; Zbl 0888.16006)] are proved. Also the authors formulate a new conjecture about the structure of \(S(G,k)\).
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 1203911
zbMATH Keywords: finite groups of Lie type
zbMATH Keywords: endomorphism algebras
zbMATH Keywords: Kazhdan-Lusztig cells
zbMATH Keywords: stratifications
reviewed by: Ahmed A. Khammash
MaRDI profile type: Publication
OpenAlex ID: W2094257727
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DOI: 10.1006/JABR.1997.7325
description: scientific article; zbMATH DE number 1203911