The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems

Author : Pavel Etingof
Publisher : OUP Oxford
ISBN 13 : 0191523925
Total Pages : 152 pages
Book Rating : 4.22/5 ( download)

DOWNLOAD NOW!

Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by Pavel Etingof and published by OUP Oxford. This book was released on 2005-03-24 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

Author : P. I. Etingof
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.50/5 ( download)

DOWNLOAD NOW!

Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by P. I. Etingof and published by . This book was released on 2005 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Andrew Pressley
Publisher : Cambridge University Press
ISBN 13 : 9781139437028
Total Pages : 246 pages
Book Rating : 4.2X/5 ( download)

DOWNLOAD NOW!

Download or read book Quantum Groups and Lie Theory written by Andrew Pressley and published by Cambridge University Press. This book was released on 2002-01-17 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises an overview of the material presented at the 1999 Durham Symposium on Quantum Groups and includes contributions from many of the world's leading figures in this area. It will be of interest to researchers and will also be useful as a reference text for graduate courses.

Author : Michio Jimbo
Publisher : World Scientific
ISBN 13 : 9789810201210
Total Pages : 740 pages
Book Rating : 4.14/5 ( download)

DOWNLOAD NOW!

Download or read book Yang-Baxter Equation in Integrable Systems written by Michio Jimbo and published by World Scientific. This book was released on 1990 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.

Author : Pavel Etingof
Publisher : Oxford University Press on Demand
ISBN 13 : 0198530684
Total Pages : 151 pages
Book Rating : 4.88/5 ( download)

DOWNLOAD NOW!

Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by Pavel Etingof and published by Oxford University Press on Demand. This book was released on 2005 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

Author : Mo-lin Ge
Publisher : World Scientific
ISBN 13 : 9814555835
Total Pages : 242 pages
Book Rating : 4.38/5 ( download)

DOWNLOAD NOW!

Download or read book Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics written by Mo-lin Ge and published by World Scientific. This book was released on 1992-05-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.

Author : Hitoshi Konno
Publisher : Springer Nature
ISBN 13 : 9811573875
Total Pages : 139 pages
Book Rating : 4.73/5 ( download)

DOWNLOAD NOW!

Download or read book Elliptic Quantum Groups written by Hitoshi Konno and published by Springer Nature. This book was released on 2020-09-14 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : L.A. Lambe
Publisher : Springer Science & Business Media
ISBN 13 : 1461541093
Total Pages : 314 pages
Book Rating : 4.97/5 ( download)

DOWNLOAD NOW!

Download or read book Introduction to the Quantum Yang-Baxter Equation and Quantum Groups: An Algebraic Approach written by L.A. Lambe and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given. The material here not specifically cited can be found for the most part in [Sweedler, 1969] in one form or another, with a few exceptions. A great deal of emphasis is placed on the coalgebra which is the dual of n x n matrices over a field. This is the most basic example of a coalgebra for our purposes and is at the heart of most algebraic constructions described in this book. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation. For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum groups.

Author : Atsuo Kuniba
Publisher : Springer Nature
ISBN 13 : 981193262X
Total Pages : 330 pages
Book Rating : 4.25/5 ( download)

DOWNLOAD NOW!

Download or read book Quantum Groups in Three-Dimensional Integrability written by Atsuo Kuniba and published by Springer Nature. This book was released on 2022-09-25 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac–Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang–Baxter equation, and its solution due to work by Kapranov–Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré–Birkhoff–Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang–Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.

Author : Louis H. Kauffman
Publisher : American Mathematical Soc.
ISBN 13 : 0821838202
Total Pages : 186 pages
Book Rating : 4.04/5 ( download)

DOWNLOAD NOW!

Download or read book Hopf Algebras and Generalizations written by Louis H. Kauffman and published by American Mathematical Soc.. This book was released on 2007 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science. This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.