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＜電子ブック＞
A Double Hall Algebra Approach to Affine Quantum Schur–Weyl Theory / Bangming Deng, Jie Du, Qiang Fu
(London Mathematical Society Lecture Note Series ; 401)

出版者	Cambridge : Cambridge University Press
出版年	2012
大きさ	1 online resource (216 pages) : digital, PDF file(s)
著者標目	*Deng, Bangming author Du, Jie author Fu, Qiang author
件　名	LCSH:Schur functions LCSH:Weyl groups LCSH:Representations of Lie groups LCSH:Affine algebraic groups
一般注記	Title from publisher's bibliographic system (viewed on 11 Nov 2016) The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of 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 ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality HTTP:URL=http://dx.doi.org/10.1017/CBO9781139226660

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