Elliptic Quantum Groups - Representations and Related Geometry (Paperback, 1st ed. 2020)

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.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Series:	SpringerBriefs in Mathematical Physics, 37
Release date:	September 2020
First published:	2020
Authors:	Hitoshi Konno
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	131
Edition:	1st ed. 2020
ISBN-13:	978-981-15-7386-6
Categories:	Books > Science & Mathematics > Physics > General Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Books > Science & Mathematics > Mathematics > Applied mathematics > Mathematical modelling Promotions
LSN:	981-15-7386-7
Barcode:	9789811573866

Is the information for this product incomplete, wrong or inappropriate? Let us know about it.

Does this product have an incorrect or missing image? Send us a new image.

Is this product missing categories? Add more categories.

Review This Product

No reviews yet - be the first to create one!