A double Hall algebra approach to affine quantum Schur-Weyl theory.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1269.20045
author: Bangming Deng
author: Jie Du
author: Qiang Fu
publication date: 2012-07-26T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.4619
Mathematics Subject Classification ID: 20G43
Mathematics Subject Classification ID: 17-02
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 6059853
zbMATH Keywords: Ringel-Hall algebras
zbMATH Keywords: affine quantum Schur algebras
zbMATH Keywords: quantum loop algebras
zbMATH Keywords: affine Hecke algebras
zbMATH Keywords: BLM bases
MaRDI profile type: Publication
arXiv ID: 1010.4619
arXiv classification: math.QA
arXiv classification: math.RA
arXiv classification: math.RT
title: A double Hall algebra approach to affine quantum Schur-Weyl theory.
published in: London Mathematical Society Lecture Note Series
review text: The theory of Schur-Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text discusses affine \(q\)-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur-Weyl theory. Various algebraic structures are discussed, including double Ringel-Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The book investigates the affine quantum Schur-Weyl duality on three levels. This includes the affine quantum Schur-Weyl reciprocity, the bridging role of affine \(q\)-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel-Hall algebra with a proof of the classical case. -- This text is very useful for researchers in algebra and graduate students who want to master Ringel-Hall algebras and Schur-Weyl duality.
reviewed by: Hu Jun
description: scientific article; zbMATH DE number 6059853