Affine Lie Algebras, Weight Multiplicities, and Branching Rules
Affine Lie Algebras, Weight Multiplicities, and Branching Rules

Author: Sam Kass

Publisher: Univ of California Press

Published: 1990-01-01

Total Pages: 312

ISBN-13: 9780520067684

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00 This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference. This practical treatise is an introduction to the mathematics and physics of affine Kac-Moody algebras. It is the result of an unusual interdisciplinary effort by two physicists and two mathematicians to make this field understandable to a broad readership and to illuminate the connections among seemingly disparate domains of mathematics and physics that are tantalizingly suggested by the ubiquity of Lie theory. The book will be useful to Lie algebraists, high energy physicists, statistical mechanics, and number theorists. Volume One contains a description of Kac-Moody Lie algebras, and especially the affine algebras and their representations; the results of extensive computations follow in Volume Two, which is spiral bound for easy reference.

Affine Lie Algebras and Quantum Groups
Affine Lie Algebras and Quantum Groups

Author: Jürgen Fuchs

Publisher: Cambridge University Press

Published: 1995-03-09

Total Pages: 452

ISBN-13: 9780521484121

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This is an introduction to the theory of affine Lie Algebras, to the theory of quantum groups, and to the interrelationships between these two fields that are encountered in conformal field theory.

Algebraic Methods in Physics
Algebraic Methods in Physics

Author: Yvan Saint-Aubin

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 268

ISBN-13: 146130119X

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This book pays tribute to two pioneers in the field of Mathematical physics, Jiri Patera and Pavel Winternitz of the CRM. Each has contributed more than forty years to the subject of mathematical physics, particularly to the study of algebraic methods.

Recent Developments in Quantum Affine Algebras and Related Topics
Recent Developments in Quantum Affine Algebras and Related Topics

Author: Naihuan Jing

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 482

ISBN-13: 0821811991

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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.

Conformal Field Theory
Conformal Field Theory

Author: Philippe Francesco

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 908

ISBN-13: 1461222567

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Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Symmetries, Lie Algebras and Representations
Symmetries, Lie Algebras and Representations

Author: Jürgen Fuchs

Publisher: Cambridge University Press

Published: 2003-10-07

Total Pages: 464

ISBN-13: 9780521541190

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This book gives an introduction to Lie algebras and their representations. Lie algebras have many applications in mathematics and physics, and any physicist or applied mathematician must nowadays be well acquainted with them.

Dualities and Representations of Lie Superalgebras
Dualities and Representations of Lie Superalgebras

Author: Shun-Jen Cheng

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 323

ISBN-13: 0821891189

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This book gives a systematic account of the structure and representation theory of finite-dimensional complex Lie superalgebras of classical type and serves as a good introduction to representation theory of Lie superalgebras. Several folklore results are rigorously proved (and occasionally corrected in detail), sometimes with new proofs. Three important dualities are presented in the book, with the unifying theme of determining irreducible characters of Lie superalgebras. In order of increasing sophistication, they are Schur duality, Howe duality, and super duality. The combinatorics of symmetric functions is developed as needed in connections to Harish-Chandra homomorphism as well as irreducible characters for Lie superalgebras. Schur-Sergeev duality for the queer Lie superalgebra is presented from scratch with complete detail. Howe duality for Lie superalgebras is presented in book form for the first time. Super duality is a new approach developed in the past few years toward understanding the Bernstein-Gelfand-Gelfand category of modules for classical Lie superalgebras. Super duality relates the representation theory of classical Lie superalgebras directly to the representation theory of classical Lie algebras and thus gives a solution to the irreducible character problem of Lie superalgebras via the Kazhdan-Lusztig polynomials of classical Lie algebras.