Abstract Kazhdan-Lusztig theories
type: Item
instance of: scholarly article
title: Abstract Kazhdan-Lusztig theories
zbMATH Open document ID: 0801.20013
author: Edward Cline
author: Leonard L. Scott
author: Brian J. Parshall
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1994-12-04T00:00:00Z
review text: The authors prove two main results: 1) They show that the Lusztig conjecture is equivalent to the simple assertion that \(\text{Ext}^ 1_ G(L(\lambda),L(\lambda')) \neq 0\) for \(p\)-regular dominant weights \(\lambda\) and \(\lambda'\) which are mirror images of one another in adjacent \(p\)-alcoves and which satisfy the Jantzen condition. 2) They give a new way of computing Ext-groups in highest weight categories.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G10
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 549623
zbMATH Keywords: Kazhdan-Lusztig polynomial
zbMATH Keywords: Yoneda Ext group
zbMATH Keywords: Lusztig conjecture
zbMATH Keywords: \(p\)- regular dominant weights
zbMATH Keywords: \(p\)-alcoves
zbMATH Keywords: highest weight categories
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225846
OpenAlex ID: W2119895559
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DOI: 10.2748/TMJ/1178225846
description: scientific article; zbMATH DE number 549623