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konno hitoshi - elliptic quantum groups

Elliptic Quantum Groups Representations and Related Geometry




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Springer

Pubblicazione: 09/2020
Edizione: 1st ed. 2020





Trama

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.




Sommario

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.










Altre Informazioni

ISBN:

9789811573866

Condizione: Nuovo
Collana: SpringerBriefs in Mathematical Physics
Dimensioni: 235 x 155 mm Ø 454 gr
Formato: Brossura
Illustration Notes:XIII, 131 p. 3 illus.
Pagine Arabe: 131
Pagine Romane: xiii


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