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Elliptic Quantum Groups : Representations and Related Geometry by Hitoshi Konno is a nonfiction available to read on EtoBox.

What is Elliptic Quantum Groups : Representations and Related Geometry about?

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

Who reads Elliptic Quantum Groups : Representations and Related Geometry?

Author

Hitoshi Konno

Publisher

Springer Singapore : Imprint: Springer

Published

2020

Language

EN

ISBN

9789811573873

Category

nonfiction

Subjects

Science, Mathematics, Physics