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Elliptic quantum groupsrepresentatio...

Konno, Hitoshi.

Elliptic quantum groupsrepresentations and related geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic quantum groupsby Hitoshi Konno.
Reminder of title:	representations and related geometry /
Author:	Konno, Hitoshi.
Published:	Singapore :Springer Singapore :2020.
Description:	xiii, 131 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Quantum groups.
Online resource:	https://doi.org/10.1007/978-981-15-7387-3
ISBN:	9789811573873$q(electronic bk.)

Elliptic quantum groupsrepresentations and related geometry /
Konno, Hitoshi.

Elliptic quantum groupsrepresentations and related geometry /[electronic resource] :by Hitoshi Konno. - Singapore :Springer Singapore :2020. - xiii, 131 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.372197-1757 ;. - SpringerBriefs in mathematical physics ;v.1..

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.

This is the first book on elliptic quantum groups, i.e., 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.

ISBN: 9789811573873$q(electronic bk.)

Standard No.: 10.1007/978-981-15-7387-3doiSubjects--Topical Terms:

190852
Quantum groups.

LC Class. No.: QC174.17.G7 / K66 2020

Dewey Class. No.: 530.12

Elliptic quantum groupsrepresentations and related geometry /
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505 0 $a 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.
520 $a This is the first book on elliptic quantum groups, i.e., 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.
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