Introduction to Quantum Groups and Crystal Bases
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Introduction to Quantum Groups and Crystal Bases by Jin Hong
The notion of a ""quantum group"" was introduced by V.G. Dinfel&dacute; and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of ""crystal bases"" or ""canonical bases"" developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups. 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.
Book by Hong and Kang is the first expository text which gives a detailed account on the relationship between crystal bases and combinatoricsThis book provides an accessible and ""crystal clear"" introduction and overview of the relatively new subject of quantum groups and crystal bases, ... It will be an indispensable companion to the research papers."" — Mathematical Reviews
Jin Hong, Korea Institute for Advanced Study, Seoul, Korea.
Seok-Jin Kang, Korea Institute for Advanced Study, Seoul, Korea.
Seok-Jin Kang, Korea Institute for Advanced Study, Seoul, Korea.
| SKU | Unavailable |
| ISBN 13 | 9781470479756 |
| ISBN 10 | 1470479753 |
| Title | Introduction to Quantum Groups and Crystal Bases |
| Author | Jin Hong |
| Series | Graduate Studies In Mathematics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | American Mathematical Society |
| Year published | 2002-01-31 |
| Number of pages | 307 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |