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A Double Hall Algebra Approach to Affine Quantum Schur–Weyl Theory

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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.

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Detail Information

Series Title

London Mathematical Society Lecture Note Series (401)

Call Number

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Publisher

: Cambridge University Press., 2013

Collation

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Language

English

ISBN/ISSN

9781139226660

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

Mathematics (general), Mathematics, Algebra

Specific Detail Info

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Statement of Responsibility

Qiang Fu, Jie Du,Bangming Deng

Other Information

Cataloger

Arin

Source

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Validator

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Digital Object Identifier (DOI)

https://doi.org/10.1017/CBO9781139226660

Journal Volume

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Journal Issue

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