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Symmetries Integrable Systems And Representations

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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.

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.

Algebraic And Analytic Aspects Of Integrable Systems And Painleve Equations

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Author : Anton Dzhamay
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-28

Algebraic And Analytic Aspects Of Integrable Systems And Painleve Equations 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 2015-10-28 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painlevé Equations, held on January 18, 2014, at the Joint Mathematics Meetings in Baltimore, MD. The theory of integrable systems has been at the forefront of some of the most important developments in mathematical physics in the last 50 years. The techniques to study such systems have solid foundations in algebraic geometry, differential geometry, and group representation theory. Many important special solutions of continuous and discrete integrable systems can be written in terms of special functions such as hypergeometric and basic hypergeometric functions. The analytic tools developed to study integrable systems have numerous applications in random matrix theory, statistical mechanics and quantum gravity. One of the most exciting recent developments has been the emergence of good and interesting discrete and quantum analogues of classical integrable differential equations, such as the Painlevé equations and soliton equations. Many algebraic and analytic ideas developed in the continuous case generalize in a beautifully natural manner to discrete integrable systems. The editors have sought to bring together a collection of expository and research articles that represent a good cross section of ideas and methods in these active areas of research within integrable systems and their applications.

Symmetry Representation Theory And Its Applications

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Author : Roger Howe
language : en
Publisher: Springer
Release Date : 2015-01-04

Symmetry Representation Theory And Its Applications written by Roger Howe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-04 with Mathematics categories.

Nolan Wallach's mathematical research is remarkable in both its breadth and depth. His contributions to many fields include representation theory, harmonic analysis, algebraic geometry, combinatorics, number theory, differential equations, Riemannian geometry, ring theory, and quantum information theory. The touchstone and unifying thread running through all his work is the idea of symmetry. This volume is a collection of invited articles that pay tribute to Wallach's ideas, and show symmetry at work in a large variety of areas. The articles, predominantly expository, are written by distinguished mathematicians and contain sufficient preliminary material to reach the widest possible audiences. Graduate students, mathematicians, and physicists interested in representation theory and its applications will find many gems in this volume that have not appeared in print elsewhere. Contributors: D. Barbasch, K. Baur, O. Bucicovschi, B. Casselman, D. Ciubotaru, M. Colarusso, P. Delorme, T. Enright, W.T. Gan, A Garsia, G. Gour, B. Gross, J. Haglund, G. Han, P. Harris, J. Hong, R. Howe, M. Hunziker, B. Kostant, H. Kraft, D. Meyer, R. Miatello, L. Ni, G. Schwarz, L. Small, D. Vogan, N. Wallach, J. Wolf, G. Xin, O. Yacobi.

Calogero Moser Systems And Representation Theory

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Author : Pavel I. Etingof
language : en
Publisher: European Mathematical Society
Release Date : 2007

Calogero Moser Systems And Representation Theory written by Pavel I. Etingof and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.

Discrete Systems And Integrability

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Author : J. Hietarinta
language : en
Publisher: Cambridge University Press
Release Date : 2016-09

Discrete Systems And Integrability written by J. Hietarinta and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09 with Mathematics categories.

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Partition Functions And Automorphic Forms

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Author : Valery A. Gritsenko
language : en
Publisher: Springer Nature
Release Date : 2020-07-09

Partition Functions And Automorphic Forms written by Valery A. Gritsenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference

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Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 1993-07-31

Differential Geometric Methods In Theoretical Physics Proceedings Of The Xxi International Conference written by Chen Ning Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-07-31 with categories.

This volume contains intense studies on Quantum Groups, Knot Theory, Statistical Mechanics, Conformal Field Theory, Differential Geometry and Differential Equation Methods and so on. It has contributions by renowned experts and covers most of the recent developments in these fields.

Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications

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Author : Alexey P Isaev
language : en
Publisher: World Scientific
Release Date : 2020-07-16

Theory Of Groups And Symmetries Representations Of Groups And Lie Algebras Applications written by Alexey P Isaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-16 with Science categories.

This book is a sequel to the book by the same authors entitled Theory of Groups and Symmetries: Finite Groups, Lie Groups, and Lie Algebras.The presentation begins with the Dirac notation, which is illustrated by boson and fermion oscillator algebras and also Grassmann algebra. Then detailed account of finite-dimensional representations of groups SL(2, C) and SU(2) and their Lie algebras is presented. The general theory of finite-dimensional irreducible representations of simple Lie algebras based on the construction of highest weight representations is given. The classification of all finite-dimensional irreducible representations of the Lie algebras of the classical series sℓ(n, C), so(n, C) and sp(2r, C) is exposed.Finite-dimensional irreducible representations of linear groups SL(N, C) and their compact forms SU(N) are constructed on the basis of the Schur-Weyl duality. A special role here is played by the theory of representations of the symmetric group algebra C[Sr] (Schur-Frobenius theory, Okounkov-Vershik approach), based on combinatorics of Young diagrams and Young tableaux. Similar construction is given for pseudo-orthogonal groups O(p, q) and SO(p, q), including Lorentz groups O(1, N-1) and SO(1, N-1), and their Lie algebras, as well as symplectic groups Sp(p, q). The representation theory of Brauer algebra (centralizer algebra of SO(p, q) and Sp(p, q) groups in tensor representations) is discussed.Finally, the covering groups Spin(p, q) for pseudo-orthogonal groups SO↑(p, q) are studied. For this purpose, Clifford algebras in spaces Rp, q are introduced and representations of these algebras are discussed.

Symmetries Integrable Systems And Representations

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