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A Double Hall Algebra Approach to Affine Quantum Schur-Weyl Theory (London Mathematical Society Lecture Note Series)

Deng, Bangming; Du, Jie; Fu, Qiang

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ISBN 10: 1107608600 / ISBN 13: 9781107608603
Published by Cambridge University Press 2013-09-16, 2013
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Bibliographic Details

Title: A Double Hall Algebra Approach to Affine ...

Publisher: Cambridge University Press 2013-09-16

Publication Date: 2013

Binding: Paperback

Book Condition:New

Edition: 1.

About this title

Synopsis:

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.

Book Description:

Schur-Weyl duality has had a profound influence over many areas of mathematics. This text is original in presenting an algebraic approach to the theory in the quantum affine case. Three levels of duality are investigated making this text ideal for researchers and graduate students who wish to master the theory.

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