\(q\)-Schur algebras, asymptotic forms, and quantum \(SL_ n\)
type: Item
instance of: scholarly article
title: \(q\)-Schur algebras, asymptotic forms, and quantum \(SL_ n\)
zbMATH Open document ID: 0855.17007
author: Jie Du
published in: Journal of Algebra
publication date: 1997-02-11T00:00:00Z
review text: An important application of Kazhdan-Lusztig bases and positivity properties for Hecke algebras are the asymptotic methods introduced by Lusztig in the study of cell classification of affine Weyl groups and representations of Hecke algebras. Following the author's previous work, this paper is an attempt to investigate asymptotic methods for \(q\)-Schur algebras and related quantum groups. He introduces some \(\mathbb{Z}\)-free algebras \({\mathcal T} (n, r)\) of finite rank, called the asymptotic forms of \(q\)-Schur algebras, and studies their structure and representations. Also he shows how these algebras are linked with a certain asymptotic form for the quantum special linear group and how they behave in forming the completion of the quantized enveloping algebras for \(GL_n\) via \(q\)-Schur algebras.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 823510
zbMATH Keywords: Kazhdan-Lusztig bases
zbMATH Keywords: Hecke algebras
zbMATH Keywords: asymptotic methods
zbMATH Keywords: \(q\)-Schur algebras
zbMATH Keywords: quantum groups
zbMATH Keywords: asymptotic forms
zbMATH Keywords: representations
zbMATH Keywords: quantum special linear group
zbMATH Keywords: quantized enveloping algebras
MaRDI profile type: Publication
full work available at URL: jabr.1995.1304
OpenAlex ID: W2066514041
DOI: 10.1006/JABR.1995.1304
description: scientific article; zbMATH DE number 823510