| Description |
1 online resource |
| Series |
SpringerBriefs in Mathematical Physics ; volume 37 |
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SpringerBriefs in mathematical physics ; v. 37.
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| 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 |
| Summary |
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 authors recent study showed that these elliptic weight functions are identified with Okounkovs elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkovs 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 CFTs, 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 |
| Bibliography |
Includes bibliographical references |
| Notes |
Online resource; title from digital title page (viewed on November 05, 2020) |
| Subject |
Quantum groups.
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Elliptic functions.
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Groups & group theory.
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Algebra.
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Mathematical modelling.
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Mathematical physics.
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Mathematics -- Algebra -- Abstract.
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Mathematics -- Applied.
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Science -- Mathematical Physics.
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Quantum groups
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Elliptic functions
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Algebra
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Group theory
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Mathematical physics
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Ordered algebraic structures
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| Form |
Electronic book
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| ISBN |
9789811573873 |
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9811573875 |
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