Representation Theory of Algebraic Groups and Quantum Groups PDF Download
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Author: Toshiaki Shoji
Publisher: American Mathematical Society(RI)
ISBN:
Category : Computers
Languages : en
Pages : 514
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Book Description
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.
Author: Toshiaki Shoji
Publisher: American Mathematical Society(RI)
ISBN:
Category : Computers
Languages : en
Pages : 514
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Book Description
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.
Author: Ken Brown
Publisher: Birkhäuser
ISBN: 303488205X
Category : Mathematics
Languages : en
Pages : 339
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Book Description
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.
Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 1461207835
Category : Mathematics
Languages : en
Pages : 540
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Book Description
Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and Drinfeld's recent fundamental contributions. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras. Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov equations.
Author: George Lusztig
Publisher: Springer Science & Business Media
ISBN: 0817647171
Category : Mathematics
Languages : en
Pages : 361
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Book Description
The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.
Author: Ross Street
Publisher: Cambridge University Press
ISBN: 1139461443
Category : Mathematics
Languages : en
Pages : 160
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Book Description
Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.
Author: Jens Carsten Jantzen
Publisher: American Mathematical Soc.
ISBN: 082184377X
Category : Mathematics
Languages : en
Pages : 594
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Book Description
Gives an introduction to the general theory of representations of algebraic group schemes. This title deals with representation theory of reductive algebraic groups and includes topics such as the description of simple modules, vanishing theorems, Borel-Bott-Weil theorem and Weyl's character formula, and Schubert schemes and lne bundles on them.
Author: Anatoli Klimyk
Publisher: Springer Science & Business Media
ISBN: 3642608965
Category : Science
Languages : en
Pages : 568
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Book Description
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.
Author: Jin Hong
Publisher: American Mathematical Soc.
ISBN: 0821828746
Category : Mathematics
Languages : en
Pages : 327
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Book Description
The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.
Author: Richard S. Elman
Publisher: American Mathematical Soc.
ISBN: 0821851616
Category : Mathematics
Languages : en
Pages : 215
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Book Description
* Brings together a wide variety of themes under a single unifying perspective The proceedings of a conference on Linear algebraic Groups and their Representations - the text gets to grips with the fundamental nature of this subject and its interaction with a wide variety of active areas in mathematics and physics.
Author: Shahn Majid
Publisher: Cambridge University Press
ISBN: 0521010411
Category : Mathematics
Languages : en
Pages : 183
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Book Description
Self-contained introduction to quantum groups as algebraic objects, suitable as a textbook for graduate courses.
