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SpringerBriefs in Mathematical Physics

Elliptic Quantum Groups

Representations and Related Geometry

Authors: Konno, Hitoshi

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  • Provides the first survey of elliptic quantum groups
  • Describes the elliptic quantum group concretely and pedagogically in the simplest setting
  • Contains finite and infinite dimensional representations along with  very recent results on geometric representations.
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  • ISBN 978-981-15-7387-3
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About this book

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-981-15-7387-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase Institutional customers should get in touch with their account manager
Softcover $59.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Elliptic Quantum Groups
Book Subtitle
Representations and Related Geometry
Authors
Series Title
SpringerBriefs in Mathematical Physics
Series Volume
37
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-7387-3
DOI
10.1007/978-981-15-7387-3
Softcover ISBN
978-981-15-7386-6
Series ISSN
2197-1757
Edition Number
1
Number of Pages
XIII, 131
Number of Illustrations
3 b/w illustrations
Topics