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Elliptic quantum groups = representa...

Konno, Hitoshi.

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Elliptic quantum groups = representations and related geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Elliptic quantum groups/ by 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.
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Quantum groups. -
Online resource:	https://doi.org/10.1007/978-981-15-7387-3
ISBN:	9789811573873

Elliptic quantum groups = representations 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.37..

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

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

629837
Quantum groups.

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

Dewey Class. No.: 530.12

Elliptic quantum groups = representations and related geometry /
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100 1 $a Konno, Hitoshi. $3 3504471
245 1 0 $a Elliptic quantum groups $h [electronic resource] : $b representations and related geometry / $c by Hitoshi Konno.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a xiii, 131 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.37
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.
650 0 $a Quantum groups. $3 629837
650 0 $a Elliptic functions. $3 576021
650 1 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Order, Lattices, Ordered Algebraic Structures. $3 896039
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in mathematical physics ; $v v.37. $3 3504472
856 4 0 $u https://doi.org/10.1007/978-981-15-7387-3
950 $a Physics and Astronomy (SpringerNature-11651)