Quantum Groups In Three Dimensional Integrability
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Quantum Groups In Three Dimensional Integrability
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Author : Atsuo Kuniba
language : en
Publisher: Springer Nature
Release Date : 2022-09-25
Quantum Groups In Three Dimensional Integrability written by Atsuo Kuniba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-25 with Science categories.
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.
Elliptic Quantum Groups
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Author : Hitoshi Konno
language : en
Publisher: Springer Nature
Release Date : 2020-09-14
Elliptic Quantum Groups written by Hitoshi Konno and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-14 with Science categories.
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.
Differential Geometric Methods In Theoretical Physics Proceedings Of The Xx International Conference In 2 Volumes
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Author : Sultan Catto
language : en
Publisher: World Scientific
Release Date : 1992-01-27
Differential Geometric Methods In Theoretical Physics Proceedings Of The Xx International Conference In 2 Volumes written by Sultan Catto and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-27 with categories.
This proceedings reports on some of the most recent advances on the interaction between Differential Geometry and Theoretical Physics, a very active and exciting area of contemporary research.The papers are grouped into the following four broad categories: Geometric Methods, Noncommutative Geometry, Quantum Gravity and Topological Quantum Field Theory. A few of the topics covered are Chern-Simons Theory and Generalizations, Knot Invariants, Models of 2D Gravity, Quantum Groups and Strings on Black Holes.
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices
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Author : Anton Dzhamay
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-06-26
Algebraic And Geometric Aspects Of Integrable Systems And Random Matrices written by Anton Dzhamay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-26 with Mathematics categories.
This volume contains the proceedings of the AMS Special Session on Algebraic and Geometric Aspects of Integrable Systems and Random Matrices, held from January 6-7, 2012, in Boston, MA. The very wide range of topics represented in this volume illustrates
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics
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Author : Pramod M. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-27
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics written by Pramod M. Achar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.
Integrability And Quantization
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Author : M. Asorey
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Integrability And Quantization written by M. Asorey and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Science categories.
Integrability and Quantization
Xvith International Congress On Mathematical Physics
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Author : Pavel Exner
language : en
Publisher: World Scientific
Release Date : 2010
Xvith International Congress On Mathematical Physics written by Pavel Exner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The International Congress on Mathematical Physics is the flagship conference in this exciting field. Convening every three years, it gives a survey on the progress achieved in all branches of mathematical physics. It also provides a superb platform to discuss challenges and new ideas. The present volume collects material from the XVIth ICMP which was held in Prague, August 2009, and features most of the plenary lectures and invited lectures in topical sessions as well as information on other parts of the congress program. This volume provides a broad coverage of the field of mathematical physics, from dominantly mathematical subjects to particle physics, condensed matter, and application of mathematical physics methods in various areas such as astrophysics and ecology, amongst others.
Yang Baxter Equation In Integrable Systems
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Author : Michio Jimbo
language : en
Publisher: World Scientific
Release Date : 1990
Yang Baxter Equation In Integrable Systems written by Michio Jimbo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Science categories.
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.
Integrability Of Nonlinear Systems
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Author : Yvette Kosmann-Schwarzbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-17
Integrability Of Nonlinear Systems written by Yvette Kosmann-Schwarzbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-17 with Science categories.
The lectures that comprise this volume constitute a comprehensive survey of the many and various aspects of integrable dynamical systems. The present edition is a streamlined, revised and updated version of a 1997 set of notes that was published as Lecture Notes in Physics, Volume 495. This volume will be complemented by a companion book dedicated to discrete integrable systems. Both volumes address primarily graduate students and nonspecialist researchers but will also benefit lecturers looking for suitable material for advanced courses and researchers interested in specific topics.
Quantum Mechanics Of Fundamental Systems 2
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Author : Claudio Teitelboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quantum Mechanics Of Fundamental Systems 2 written by Claudio Teitelboim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Studies based on a meeting held at the Centro de Estudios Cientificos de Santiago, Dec. 17-20, 1987, review new developments in the field. Areas covered include: anomalous Jacobians and the vector anomaly; string phenomenology; quantum groups, integrable theories, and conformed models, small handles