Author : Toshiaki Shoji
Publisher : American Mathematical Society(RI)
Page : 514 pages
File Size : 15,49 MB
Release : 2004
Category : Computers
ISBN :
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
Page : 339 pages
File Size : 25,9 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 303488205X
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 : Peter Woit
Publisher : Springer
Page : 659 pages
File Size : 17,36 MB
Release : 2017-11-01
Category : Science
ISBN : 3319646125
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. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
Author : A. Broer
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 48,11 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401591318
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, resulting in great progress in these representation theories. Conversely, a great stimulus has been given to the development of such geometric theories as D-modules, perverse sheafs and equivariant intersection cohomology. The range of topics covered is wide, from equivariant Chow groups, decomposition classes and Schubert varieties, multiplicity free actions, convolution algebras, standard monomial theory, and canonical bases, to annihilators of quantum Verma modules, modular representation theory of Lie algebras and combinatorics of representation categories of Harish-Chandra modules.
Author : Christian Kassel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 22,28 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461207835
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 : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 37,49 MB
Release : 2006
Category : Mathematics
ISBN : 0821839241
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.
Author :
Publisher : Elsevier
Page : 357 pages
File Size : 39,78 MB
Release : 1996-09-27
Category : Mathematics
ISBN : 0080526950
This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.Presents several different points of view on key topics in representation theory, from internationally known experts in the field
Author : Anatoli Klimyk
Publisher : Springer Science & Business Media
Page : 568 pages
File Size : 42,44 MB
Release : 2012-12-06
Category : Science
ISBN : 3642608965
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 : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 45,5 MB
Release : 2008-07-31
Category : Mathematics
ISBN : 0521889693
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author : Roger W. Carter
Publisher : Cambridge University Press
Page : 203 pages
File Size : 20,48 MB
Release : 1998-09-03
Category : Mathematics
ISBN : 0521643252
This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
