Elliptic Quantum Groups : Representations and Related Geometry / by Hitoshi Konno.

Format:

Book

Author/Creator:

Konno, Hitoshi, author.

Contributor:

SpringerLink (Online service)

Series:

Physics and Astronomy (SpringerNature-11651)

SpringerBriefs in mathematical physics 2197-1757 ; 37.

SpringerBriefs in Mathematical Physics, 2197-1757 ; 37

Language:

English

Subjects (All):

Mathematical physics.

Group theory.

Algebra.

Ordered algebraic structures.

Mathematical Physics.

Group Theory and Generalizations.

Order, Lattices, Ordered Algebraic Structures.

Mathematical Applications in the Physical Sciences.

Local Subjects:

Mathematical Physics.

Group Theory and Generalizations.

Order, Lattices, Ordered Algebraic Structures.

Mathematical Applications in the Physical Sciences.

Physical Description:

1 online resource (XIII, 131 pages) : 3 illustrations.

Edition:

First edition 2020.

Contained In:

Springer Nature eBook

Place of Publication:

Singapore : Springer Singapore : Imprint: Springer, 2020.

System Details:

text file PDF

Summary:

This is the first book on elliptic quantum groups, id est, quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author's recent study showed that these elliptic weight functions are identified with Okounkov's elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov's geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT's, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book.

Contents:

Preface

Acknowledgements

Chapter 1: Introduction

Chapter 2: Elliptic Quantum Group

Chapter 3: The H-Hopf Algebroid Structure of

Chapter 4: Representations of

Chapter 5: The Vertex Operators

Chapter 6: Elliptic Weight Functions

Chapter 7: Tensor Product Representation

Chapter 8: Elliptic q-KZ Equation

Chapter 9: Related Geometry

Appendix A

Appendix B

Appendix C

Appendix D

Appendix E

References.

Other Format:

Printed edition:

ISBN:

978-981-15-7387-3

9789811573873

Access Restriction:

Restricted for use by site license.