Representation Theory Mathematical Physics And Integrable Systems
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Representation Theory Mathematical Physics And Integrable Systems
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Author : Anton Alekseev
language : en
Publisher: Springer Nature
Release Date : 2022-02-05
Representation Theory Mathematical Physics And Integrable Systems written by Anton Alekseev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-05 with Mathematics categories.
Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.
Symmetries Integrable Systems And Representations
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Author : Kenji Iohara
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symmetries Integrable Systems And Representations written by Kenji Iohara 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 Mathematics categories.
This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Symmetries Integrable Systems And Representations
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Author : Kenji Iohara
language : en
Publisher: Springer
Release Date : 2012-12-05
Symmetries Integrable Systems And Representations written by Kenji Iohara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-05 with Mathematics categories.
This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.
Basics Of Representation Theory
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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.
From Representation Theory To Mathematical Physics And Back
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Author : Mikhail Khovanov
language : en
Publisher: American Mathematical Society
Release Date : 2025-05-14
From Representation Theory To Mathematical Physics And Back written by Mikhail Khovanov 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 2025-05-14 with Mathematics categories.
This volume is a proceedings of a workshop at the Simons Center for Geometry and Physics from May 31– June 4, 2022. The workshop highlighted progress in the areas of vertex operator algebras, conformal field theory, categorification, low dimensional topology and representation theory of affine Lie algebras, loop groups, and quantum groups. In the past 40 years, string theory gave rise to the mathematical theory of vertex operator algebras, which led to the construction of representations of affine Lie algebras and the Moonshine module of the Monster group. These mathematical constructions have in turn led to ideas about 3-dimensional quantum gravity. In another direction, the discovery of the Jones polynomial led to a physical construction of 3-dimensional topological quantum field theories (TQFTs), which in turn advanced many mathematical developments in quantum groups and low dimensional topology. Louis Crane and Igor Frenkel introduced the categorification program with the goal of upgrading 3-dimensional TQFTs coming from representation theory of quantum groups to 4-dimensional TQFTs. This idea gave rise to the development of link homologies constructed from representation-theoretic, algebraic-geometric, combinatorial, and physical structures. Articles in this volume present both classical and new results related to these topics. They will be interesting to researchers and graduate students working in mathematical aspects of modern quantum field theory.
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : Pavel Etingof
language : en
Publisher: OUP Oxford
Release Date : 2005-03-24
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by Pavel Etingof and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-24 with Mathematics categories.
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.
Group Theoretical Methods For Integration Of Nonlinear Dynamical Systems
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Author : A.N. Leznov
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-04-22
Group Theoretical Methods For Integration Of Nonlinear Dynamical Systems written by A.N. Leznov 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 1992-04-22 with Mathematics categories.
The book reviews a large number of 1- and 2-dimensional equations that describe nonlinear phenomena in various areas of modern theoretical and mathematical physics. It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields. We hope that the book will be useful also for experts in hydrodynamics, solid-state physics, nonlinear optics electrophysics, biophysics and physics of the Earth. The first two chapters of the book present some results from the repre sentation theory of Lie groups and Lie algebras and their counterpart on supermanifolds in a form convenient in what follows. They are addressed to those who are interested in integrable systems but have a scanty vocabulary in the language of representation theory. The experts may refer to the first two chapters only occasionally. As we wanted to give the reader an opportunity not only to come to grips with the problem on the ideological level but also to integrate her or his own concrete nonlinear equations without reference to the literature, we had to expose in a self-contained way the appropriate parts of the representation theory from a particular point of view.
Groups And Symmetries
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Author : Yvette Kosmann-Schwarzbach
language : en
Publisher: Springer Nature
Release Date : 2022-07-16
Groups And Symmetries written by Yvette Kosmann-Schwarzbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-16 with Mathematics categories.
- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study
Elements Of Classical And Quantum Integrable Systems
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Author : Gleb Arutyunov
language : en
Publisher: Springer
Release Date : 2019-07-23
Elements Of Classical And Quantum Integrable Systems written by Gleb Arutyunov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-23 with Science categories.
Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland andRuijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.
Infinite Dimensional Algebras And Quantum Integrable Systems
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Author : Petr P. Kulish
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Infinite Dimensional Algebras And Quantum Integrable Systems written by Petr P. Kulish 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 2006-01-17 with Mathematics categories.
This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.