Recent Developments In Quantum Affine Algebras And Related Topics

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Recent Developments in Quantum Affine Algebras and Related Topics

Naihuan Jing,Kailash C. Misra
Recent Developments in Quantum Affine Algebras and Related Topics Book PDF

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 44,8 Mb
Release : 1999
Category : Affine algebraic groups
ISBN : 9780821811993

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Recent Developments in Quantum Affine Algebras and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Representations of Algebras and Related Topics

Andrzej Skowroński,Kunio Yamagata
Representations of Algebras and Related Topics Book PDF

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 48,8 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications

Yun Gao
Quantum Affine Algebras Extended Affine Lie Algebras and Their Applications Book PDF

Author : Yun Gao
Publisher : American Mathematical Soc.
Page : 314 pages
File Size : 51,9 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821845073

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Quantum Affine Algebras, Extended Affine Lie Algebras, and Their Applications by Yun Gao Pdf

This volume contains the proceedings of the conference on Quantum Affine Algebras, Extended Affine Lie Algebras, and Applications, which was held at the Banff International Research Station, Banff, Canada, from March 2-7, 2008. Many of the papers include new results on different aspects of quantum affine algebras, extended affine Lie algebras, and their applications in other areas of mathematics and physics. Any reader interested in learning about the recent developments in quantum affine algebras and extended affine Lie algebras will benefit from this book.

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi
Interactions of Quantum Affine Algebras with Cluster Algebras Current Algebras and Categorification Book PDF

Author : Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi
Publisher : Springer Nature
Page : 453 pages
File Size : 53,5 Mb
Release : 2022-03-11
Category : Mathematics
ISBN : 9783030638498

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Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification by Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi Pdf

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Representation Theory of Algebraic Groups and Quantum Groups

Akihiko Gyoja,Hiraku Nakajima,Ken-ichi Shinoda,Toshiaki Shoji,Toshiyuki Tanisaki
Representation Theory of Algebraic Groups and Quantum Groups Book PDF

Author : Akihiko Gyoja,Hiraku Nakajima,Ken-ichi Shinoda,Toshiaki Shoji,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 52,7 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780817646974

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Representation Theory of Algebraic Groups and Quantum Groups by Akihiko Gyoja,Hiraku Nakajima,Ken-ichi Shinoda,Toshiaki Shoji,Toshiyuki Tanisaki Pdf

Invited articles by top notch experts Focus is on topics in representation theory of algebraic groups and quantum groups Of interest to graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics

Vertex Operator Algebras, Number Theory and Related Topics

Matthew Krauel,Michael Tuite,Gaywalee Yamskulna
Vertex Operator Algebras Number Theory and Related Topics Book PDF

Author : Matthew Krauel,Michael Tuite,Gaywalee Yamskulna
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 48,6 Mb
Release : 2020-07-13
Category : Education
ISBN : 9781470449384

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Vertex Operator Algebras, Number Theory and Related Topics by Matthew Krauel,Michael Tuite,Gaywalee Yamskulna Pdf

This volume contains the proceedings of the International Conference on Vertex Operator Algebras, Number Theory, and Related Topics, held from June 11–15, 2018, at California State University, Sacramento, California. The mathematics of vertex operator algebras, vector-valued modular forms and finite group theory continues to provide a rich and vibrant landscape in mathematics and physics. The resurgence of moonshine related to the Mathieu group and other groups, the increasing role of algebraic geometry and the development of irrational vertex operator algebras are just a few of the exciting and active areas at present. The proceedings center around active research on vertex operator algebras and vector-valued modular forms and offer original contributions to the areas of vertex algebras and number theory, surveys on some of the most important topics relevant to these fields, introductions to new fields related to these and open problems from some of the leaders in these areas.

Symmetries, Integrable Systems and Representations

Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Symmetries Integrable Systems and Representations Book PDF

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

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.

Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Recent Developments in Infinite Dimensional Lie Algebras and Conformal Field Theory Book PDF

Author : Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 54,7 Mb
Release : 2002
Category : Conformal invariants
ISBN : 9780821827161

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Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory by Stephen Berman,Paul Fendley,Yi-Zhi Huang,Kailash Misra,Brian Parshall Pdf

Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.

Physics And Combinatorics, Procs Of The Nagoya 2000 Intl Workshop

Anatol N Kirillov,Nadejda Liskova
Physics And Combinatorics Procs Of The Nagoya 2000 Intl Workshop Book PDF

Author : Anatol N Kirillov,Nadejda Liskova
Publisher : World Scientific
Page : 329 pages
File Size : 55,9 Mb
Release : 2001-04-19
Category : Science
ISBN : 9789814490917

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Physics And Combinatorics, Procs Of The Nagoya 2000 Intl Workshop by Anatol N Kirillov,Nadejda Liskova Pdf

The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.

Physics and Combinatorics 2000

Anatol N. Kirillov,Nadejda Liskova
Physics and Combinatorics 2000 Book PDF

Author : Anatol N. Kirillov,Nadejda Liskova
Publisher : World Scientific
Page : 329 pages
File Size : 52,9 Mb
Release : 2001
Category : Science
ISBN : 9789810246426

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Physics and Combinatorics 2000 by Anatol N. Kirillov,Nadejda Liskova Pdf

The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in their fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.

New Trends in Quantum Integrable Systems

Boris Feigin
New Trends in Quantum Integrable Systems Book PDF

Author : Boris Feigin
Publisher : World Scientific
Page : 128 pages
File Size : 47,7 Mb
Release : 2014-05-14
Category : Electronic
ISBN : 9789814462921

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New Trends in Quantum Integrable Systems by Boris Feigin Pdf

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto Japan from 27 to 31 July 2009. As a continuation of the RIMS Research Project a Method of Algebraic Analysis in Integrable Systemsa in 2004 the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models integrable models in quantum field theory conformal field theory mathematical aspects of Bethe ansatz special functions and integrable differential/difference equations representation theory of infinite dimensional algebras integrable models and combinatorics.Through these topics the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics."

Groups of Homotopy Self-Equivalences and Related Topics

Ken-ichi Maruyama,John W. Rutter
Groups of Homotopy Self Equivalences and Related Topics Book PDF

Author : Ken-ichi Maruyama,John W. Rutter
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 49,6 Mb
Release : 2001
Category : Homotopy equivalences
ISBN : 9780821826836

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Groups of Homotopy Self-Equivalences and Related Topics by Ken-ichi Maruyama,John W. Rutter Pdf

This volume offers the proceedings from the workshop held at the University of Milan (Italy) on groups of homotopy self-equivalences and related topics. The book comprises the articles relating current research on the group of homotopy self-equivalences, homotopy of function spaces, rational homotopy theory, classification of homotopy types, and equivariant homotopy theory. Mathematicians from many areas of the globe attended the workshops to discuss their research and to share ideas. Included are two specially-written articles, by J.W. Rutter, reviewing the work done in the area of homotopy self-equivalences since 1988. Included also is a bibliography of some 122 articles published since 1988 and a list of problems. This book is suitable for both advanced graduate students and researchers.

Combinatorial and Geometric Representation Theory

Seok-Jin Kang,Kyu-Hwan Lee
Combinatorial and Geometric Representation Theory Book PDF

Author : Seok-Jin Kang,Kyu-Hwan Lee
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 50,8 Mb
Release : 2003
Category : Combinatorial analysis
ISBN : 9780821832127

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Combinatorial and Geometric Representation Theory by Seok-Jin Kang,Kyu-Hwan Lee Pdf

This volume presents the proceedings of the international conference on Combinatorial and Geometric Representation Theory. In the field of representation theory, a wide variety of mathematical ideas are providing new insights, giving powerful methods for understanding the theory, and presenting various applications to other branches of mathematics. Over the past two decades, there have been remarkable developments. This book explains the strong connections between combinatorics, geometry, and representation theory. It is suitable for graduate students and researchers interested in representation theory.

Representation Theory, Mathematical Physics, and Integrable Systems

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

Author : Anton Alekseev,Edward Frenkel,Marc Rosso,Ben Webster,Milen Yakimov
Publisher : Springer Nature
Page : 652 pages
File Size : 45,7 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.

Sugawara Operators for Classical Lie Algebras

Alexander Molev:
Sugawara Operators for Classical Lie Algebras Book PDF

Author : Alexander Molev:
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 40,9 Mb
Release : 2018-02-28
Category : Affine algebraic groups
ISBN : 9781470436599

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Sugawara Operators for Classical Lie Algebras by Alexander Molev: Pdf

The celebrated Schur-Weyl duality gives rise to effective ways of constructing invariant polynomials on the classical Lie algebras. The emergence of the theory of quantum groups in the 1980s brought up special matrix techniques which allowed one to extend these constructions beyond polynomial invariants and produce new families of Casimir elements for finite-dimensional Lie algebras. Sugawara operators are analogs of Casimir elements for the affine Kac-Moody algebras. The goal of this book is to describe algebraic structures associated with the affine Lie algebras, including affine vertex algebras, Yangians, and classical -algebras, which have numerous ties with many areas of mathematics and mathematical physics, including modular forms, conformal field theory, and soliton equations. An affine version of the matrix technique is developed and used to explain the elegant constructions of Sugawara operators, which appeared in the last decade. An affine analogue of the Harish-Chandra isomorphism connects the Sugawara operators with the classical -algebras, which play the role of the Weyl group invariants in the finite-dimensional theory.