Calogero Moser Systems And Representation Theory

Author : Pavel I. Etingof
Publisher : European Mathematical Society
Page : 108 pages
File Size : 42,7 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190345

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Calogero-Moser Systems and Representation Theory by Pavel I. Etingof Pdf

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.

Author : Jan F. van Diejen,Luc Vinet
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461212065

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Calogero—Moser— Sutherland Models by Jan F. van Diejen,Luc Vinet Pdf

In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 48,5 Mb
Release : 2008
Category : Representations of algebras
ISBN : 3037190620

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Trends in Representation Theory of Algebras and Related Topics by Andrzej Skowroński Pdf

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

Author : Roger Howe,Markus Hunziker,Jeb F. Willenbring
Publisher : Springer
Page : 538 pages
File Size : 51,6 Mb
Release : 2015-01-04
Category : Mathematics
ISBN : 9781493915903

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Symmetry: Representation Theory and Its Applications by Roger Howe,Markus Hunziker,Jeb F. Willenbring Pdf

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.

Author : Pavel Exner
Publisher : World Scientific
Page : 709 pages
File Size : 50,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814304634

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XVIth International Congress on Mathematical Physics by Pavel Exner Pdf

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.

Author : Sam Evens
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 44,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821875735

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Mathematical Aspects of Quantization by Sam Evens Pdf

This book is a collection of expository articles from the Center of Mathematics at Notre Dame's 2011 program on quantization. Included are lecture notes from a summer school on quantization on topics such as the Cherednik algebra, geometric quantization, detailed proofs of Willwacher's results on the Kontsevich graph complex, and group-valued moment maps. This book also includes expository articles on quantization and automorphic forms, renormalization, Berezin-Toeplitz quantization in the complex setting, and the commutation of quantization with reduction, as well as an original article on derived Poisson brackets. The primary goal of this volume is to make topics in quantization more accessible to graduate students and researchers.

Author : M Boiti,Luigi Martina,F Pempinelli,Barbara Prinari,Giulio Soliani
Publisher : World Scientific
Page : 568 pages
File Size : 42,9 Mb
Release : 2000-05-12
Category : Science
ISBN : 9789814493932

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Nonlinearity, Integrability And All That: Twenty Years After Needs '79 - Proceedings Of The Workshop by M Boiti,Luigi Martina,F Pempinelli,Barbara Prinari,Giulio Soliani Pdf

This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems — classical and quantum — are considered.

Author : Anonim
Publisher : World Scientific
Page : 1001 pages
File Size : 44,5 Mb
Release : 2024-06-15
Category : Electronic
ISBN : 8210379456XXX

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by Anonim Pdf

Author : Bhatia Rajendra,Pal Arup,Rangarajan G
Publisher : World Scientific
Page : 4144 pages
File Size : 41,8 Mb
Release : 2011-06-06
Category : Mathematics
ISBN : 9789814462938

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Proceedings Of The International Congress Of Mathematicians 2010 (Icm 2010) (In 4 Volumes) - Vol. I: Plenary Lectures And Ceremonies, Vols. Ii-iv: Invited Lectures by Bhatia Rajendra,Pal Arup,Rangarajan G Pdf

ICM 2010 proceedings comprises a four-volume set containing articles based on plenary lectures and invited section lectures, the Abel and Noether lectures, as well as contributions based on lectures delivered by the recipients of the Fields Medal, the Nevanlinna, and Chern Prizes. The first volume will also contain the speeches at the opening and closing ceremonies and other highlights of the Congress.

Author : Pavel Etingof,Pavel I. Etingof,Frederic Latour
Publisher : Oxford University Press on Demand
Page : 151 pages
File Size : 46,7 Mb
Release : 2005
Category : Mathematics
ISBN : 9780198530688

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The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems by Pavel Etingof,Pavel I. Etingof,Frederic Latour Pdf

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 : Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo
Publisher : World Scientific
Page : 5396 pages
File Size : 52,6 Mb
Release : 2019-02-27
Category : Mathematics
ISBN : 9789813272897

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Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by Sirakov Boyan,Souza Paulo Ney De,Viana Marcelo Pdf

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Author : Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Publisher : Springer Nature
Page : 652 pages
File Size : 44,9 Mb
Release : 2022-02-05
Category : Mathematics
ISBN : 9783030781484

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Representation Theory, Mathematical Physics, and Integrable Systems by Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov Pdf

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.

Author : Yvan Saint-Aubin,Luc Vinet
Publisher : Springer Science & Business Media
Page : 646 pages
File Size : 40,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781475736717

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Theoretical Physics at the End of the Twentieth Century by Yvan Saint-Aubin,Luc Vinet Pdf

Based on courses given at the CRM Banff summer school in 1999, this volume provides a snapshot of topics engaging theoretical physicists at the end of the twentieth century and the beginning of the twenty-first. Young physicists will find in these chapters pedagogical introductions to subjects currently active in theoretical physics, and more seasoned physicists will find a chance to share the excitement of fields outside their immediate research interests.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 595 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512886

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This is the first Supplementary volume to Kluwer's highly acclaimed Encyclopaedia of Mathematics. This additional volume contains nearly 600 new entries written by experts and covers developments and topics not included in the already published 10-volume set. These entries have been arranged alphabetically throughout. A detailed index is included in the book. This Supplementary volume enhances the existing 10-volume set. Together, these eleven volumes represent the most authoritative, comprehensive up-to-date Encyclopaedia of Mathematics available.

Author : Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss
Publisher : Cambridge University Press
Page : 367 pages
File Size : 43,9 Mb
Release : 2016-06-20
Category : Mathematics
ISBN : 9781107129542

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Noncommutative Algebraic Geometry by Gwyn Bellamy,Daniel Rogalski,Travis Schedler,J. Toby Stafford,Michael Wemyss Pdf

This book provides a comprehensive introduction to the interactions between noncommutative algebra and classical algebraic geometry.