A double Hall algebra approach to affine quantum SchurWeyl theory
 Author/Creator
 Deng, Bangming.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2012.
 Physical description
 viii, 207 p. ; 23 cm.
 Series
 London Mathematical Society lecture note series ; 401.
Access
Available online

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Unknown
QA331.7 .D46 2012

Unknown
QA331.7 .D46 2012
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Contributors
 Contributor
 Du, Jie.
 Fu, Qiang.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 201204) and index.
 Contents

 Introduction 1. Preliminaries 2. Double RingelHall algebras of cyclic quivers 3. Affine quantum Schur algebras and the SchurWeyl reciprocity 4. Representations of affine quantum Schur algebras 5. The presentation and realization problems 6. The classical (v =1) case Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The theory of SchurWeyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine qSchur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum SchurWeyl theory. To begin, various algebraic structures are discussed, including double RingelHall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum SchurWeyl duality on three levels. This includes the affine quantum SchurWeyl reciprocity, the bridging role of affine qSchur 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 RingelHall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master RingelHall algebras and SchurWeyl duality.
(source: Nielsen Book Data)
Bibliographic information
 Publication date
 2012
 Responsibility
 Bangming Deng, Jie Du, Qiang Fu.
 Series
 London Mathematical Society lecture note series ; 401
 ISBN
 1107608600
 9781107608603