Representations Of Algebraic Groups Quantum Groups And Lie Algebras
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Representations of Algebraic Groups Quantum Groups and Lie Algebras
Author | : Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups |
Publsiher | : American Mathematical Soc. |
Total Pages | : 270 |
Release | : 2006 |
Genre | : Affine algebraic groups |
ISBN | : 9780821839249 |
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Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.
Representation Theory of Algebraic Groups and Quantum Groups
Author | : Toshiaki Shoji |
Publsiher | : American Mathematical Society(RI) |
Total Pages | : 514 |
Release | : 2004 |
Genre | : Computers |
ISBN | : UOM:39015061859339 |
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A collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference. This title presents an overview of developments in representation theory of algebraic groups and quantum groups. It includes papers containing results concerning Lusztig's conjecture on cells in affine Weyl groups.
Quantum Groups and Their Representations
Author | : Anatoli Klimyk,Konrad Schmüdgen |
Publsiher | : Springer Science & Business Media |
Total Pages | : 568 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9783642608964 |
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This book start with an introduction to quantum groups for the beginner and continues as a textbook for graduate students in physics and in mathematics. It can also be used as a reference by more advanced readers. The authors cover a large but well-chosen variety of subjects from the theory of quantum groups (quantized universal enveloping algebras, quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. The book is written with potential applications in physics and mathematics in mind. The basic quantum groups and quantum algebras and their representations are given in detail and accompanied by explicit formulas. A number of topics and results from the more advanced general theory are developed and discussed.
Representation Theory of Algebraic Groups and Quantum Groups
Author | : Akihiko Gyoja,Hiraku Nakajima,Ken-ichi Shinoda,Toshiaki Shoji,Toshiyuki Tanisaki |
Publsiher | : Springer Science & Business Media |
Total Pages | : 356 |
Release | : 2010-11-25 |
Genre | : Mathematics |
ISBN | : 9780817646974 |
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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
Algebras of Functions on Quantum Groups Part I
Author | : Leonid I. Korogodski,Leonid I.. Korogodski,Yan S. Soibelman,Yan S.. Soibelman |
Publsiher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 1998 |
Genre | : Function algebras |
ISBN | : 9780821803363 |
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The text is devoted to the study of algebras of functions on quantum groups. The book includes the theory of Poisson-Lie algebras (quasi-classical version of algebras of functions on quantum groups), a description of representations of algebras of functions and the theory of quantum Weyl groups. It can serve as a text for an introduction to the theory of quantum groups and is intended for graduate students and research mathematicians working in algebra, representation theory and mathematical physics.
Lectures on Algebraic Quantum Groups
Author | : Ken Brown,Ken R. Goodearl |
Publsiher | : Birkhäuser |
Total Pages | : 339 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9783034882057 |
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This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.
Quantum Group Symmetry and Q tensor Algebras
Author | : L. C. Biedenharn,M. A. Lohe |
Publsiher | : World Scientific |
Total Pages | : 305 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9789810223311 |
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Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
Algebraic Groups and their Representations
Author | : R.W. Carter,J. Saxl |
Publsiher | : Springer Science & Business Media |
Total Pages | : 388 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9789401153089 |
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This volume contains 19 articles written by speakers at the Advanced Study Institute on 'Modular representations and subgroup structure of al gebraic groups and related finite groups' held at the Isaac Newton Institute, Cambridge from 23rd June to 4th July 1997. We acknowledge with gratitude the financial support given by the NATO Science Committee to enable this ASI to take place. Generous financial support was also provided by the European Union. We are also pleased to acknowledge funds given by EPSRC to the Newton Institute which were used to support the meeting. It is a pleasure to thank the Director of the Isaac Newton Institute, Professor Keith Moffatt, and the staff of the Institute for their dedicated work which did so much to further the success of the meeting. The editors wish to thank Dr. Ross Lawther and Dr. Nick Inglis most warmly for their help in the production of this volume. Dr. Lawther in particular made an invaluable contribution in preparing the volume for submission to the publishers. Finally we wish to thank the distinguished speakers at the ASI who agreed to write articles for this volume based on their lectures at the meet ing. We hope that the volume will stimulate further significant advances in the theory of algebraic groups.