3 edition of **Representation theory of algebraic groups and quantum groups** found in the catalog.

Representation theory of algebraic groups and quantum groups

MSJ International Reseach Institute (10th 2001 Tokyo, Japan)

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Published
**2004**
by Mathematical Society of Japan in Tokyo
.

Written in English

- Representations of algebras -- Congresses.,
- Group algebras -- Congresses.,
- Quantum groups -- Congresses.

**Edition Notes**

Statement | edited by Toshiaki Shoji ... [et al.]. |

Genre | Congresses. |

Series | Advanced studies in pure mathematics -- 40, Advanced studies in pure mathematics (Tokyo, Japan) -- 40. |

Contributions | Shoji, Toshiaki. |

Classifications | |
---|---|

LC Classifications | QA150 .M75 2004 |

The Physical Object | |

Pagination | 490 p. : |

Number of Pages | 490 |

ID Numbers | |

Open Library | OL22620404M |

ISBN 10 | 4931469256 |

This book provides a treatment of the theory of quantum groups (quantized universal enveloping algebras and quantized algebras of functions) and q-deformed algebras (q-oscillator algebras), their representations and corepresentations, and noncommutative differential calculus. Operational Quantum Theory I is a distinguished work on quantum theory at an advanced algebraic level. Quantum theory (nonrelativistic quantum mechanics and quantum theory) is developed from a representation theory of lie group and lie algebraic operations acting on both finite and infinite dimensional vector spaces.

This volume contains the proceedings of the tenth international conference on Representation Theory of Algebraic Groups and Quantum Groups, held August 2–6, , at Nagoya University, Nagoya, Japan. The survey articles and original papers contained in this volume offer a comprehensive view of current developments in the field. Representation Theory of Algebraic Groups and Quantum Groups, T. Shoji, M. Kashiwara, N. Kawanaka, G. Lusztig and K. Shinoda, eds. (Tokyo: Mathematical Society of Japan, ), 3 pp. Representation Theory of Algebraic Groups and Quantum Groups – Program.

no hope of understanding representation theory. Set aside a few hours to get it throughyourthickskull. (Believeme,it’stoughfor(everyone everyphysicisttheir((((ﬁrsttime.) Representation theory is important in physics for a billion reasons, but here is one: Hilbert spaces are complex vector spaces, so any group action on a Hilbert. Representation theory of groups, quantum groups, and operator algebras The University of Copenhagen June 1 - 5, The study of group representations has been one of the main motivations behind the development of operator algebra theory since the s.

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Representation Theory of Algebraic Groups and Quantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors. This book is a collection of research and survey papers written by speakers at the Mathematical Society of Japan's 10th International Conference.

It presents a comprehensive overview of developments in representation theory of algebraic groups and quantum groups. Quantum Theory, Groups and Representations: An Introduction Peter Woit Department of Mathematics, Columbia University [email protected] The theory is developed in such a way that almost everything carries over to quantum groups.

It emphasizes the similarities between the modular representation theory and the representation theory for quantum groups at roots of unity. The chapter provides basic general definitions concerning algebraic groups and their representations.

Similarly, the quantum group U q (G) can be regarded as an algebra over the field Q(q), the field of all rational functions of an indeterminate q over Q (see below in the section on quantum groups at q = 0). The center of quantum group can be described by quantum determinant.

Representation theory. The theory is developed in such a way that almost everything carries over to quantum groups. It emphasizes the similarities between the modular representation theory and the representation theory for quantum groups at roots of unity.

The chapter provides basic general definitions concerning algebraic groups and their representations. Littlewood's Formulas for Characters of Orthogonal and Symplectic Groups (A Lascoux) A q-Analog of Schur's Q-Functions (G Tudose & M Zabrocki) Readership: Researchers and graduate students in algebraic combinatorics, representation theory and quantum groups.

The representation theory of linear algebraic groups and Lie groups extends these examples to infinite-dimensional groups, the latter being intimately related to Lie algebra representations.

The importance of character theory for finite groups has an analogue in the theory of weights for representations of Lie groups and Lie algebras.

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.

Preface.- 1 Introduction and Overview.- 2 The Group U(1) and its Representations.- 3 Two-state Systems and SU(2).- 4 Linear Algebra Review, Unitary and Orthogonal Groups.- 5 Lie Algebras and Lie Algebra Representations.- 6 The Rotation and Spin Groups in 3 and 4 Dimensions.- 7 Rotations and the Spin 1/2 Particle in a Magnetic Field.- 8 Representations of SU(2) and SO(3).- 9 Tensor Products.

See also, E. Wigner, Group Theory and its Application to the Quantum Mechanics of Atomic Spectra (Academic Press Inc., New York, ), English edition, Chaps 24 and Google Scholar; 2.

Weyl, The Classical Groups, Their Invariants and Representations (Princeton University Press, Princeton, New Jersey, ). Chapter 3 of this book. This volume contains the proceedings of two AMS Special Sessions Geometric and Algebraic Aspects of Representation Theory' and Quantum Groups and Noncommutative Algebraic Geometry' held October, at Tulane University, New Orleans, Louisiana, ed in this volume are original research and some survey articles on various aspects of representations of.

This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory.

Lie algebras Lie groups quantization quantum fields quantum mechanics representation theory Standard Model of particle physics unitary group representations two-state systems Lie algebra representations rotation and spin groups momentum and free particle fourier analysis and free particle Schroedinger representation Heisenberg group Poisson bracket and symplectic geometry.

Get this from a library. Representation theory of algebraic groups and quantum groups. [Akihiko Gyoja;] -- This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases.

This book emphasises the algebraic aspects of quantum theory and as such is an excellent complement to any of the other QM texts which emphasise the analytic material necessary to cover the Stone - Von Neumann and spectral theorems.

It is highly readable and well suited to self study. An excellent book on a rewarding s: 4. Representation Theory of Algebraic Groups and Quantum Groups. August 1 - 10, Sophia University, Tokyo.

To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g.

Next, this book discusses Lie group and Lie algebra. "The conference 'Representation Theory of Algebraic Groups and Quantum Groups' was held at Sophia University in Tokyo from August 1 to 10,as the 10th International Research Institute of the Mathematical Society of Japan (MSJ-IRI)"--Preface.

Representation Theory of Algebraic Groups and Quantum Groups, Hardcover by Gyoja, Akihiko (EDT); Nakajima, Hiraku (EDT); Shinoda, Ken-ichi (EDT); Shoji, Toshiaki (EDT); Tanisaki, Toshiyuki (EDT), ISBNISBNLike New Used, Free shipping in the US This volume contains invited articles by top-notch experts who focus on such topics as: modular representations Seller Rating: % positive.

The book includes the theory of Poisson Lie groups (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. This book can serve as a text for an introduction to the theory of quantum groups.The 12 lectures presented in Representation Theories and Algebraic Geometry focus on the very rich and powerful interplay between algebraic geometry and the representation theories of various modern mathematical structures, such as reductive groups, quantum groups, Hecke algebras, restricted Lie algebras, and their companions.

This interplay has been extensively exploited during recent years. Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups.