New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 Graduate Studies in Mathematics 2014; 432 pp; hardcover Volume: 155 ISBN-10: 1-4704-0966-6 ISBN-13: 978-1-4704-0966-1 List Price: US$79 Member Price: US$63.20 Order Code: GSM/155 Not yet published.Expected publication date is September 22, 2014. See also: Analytic Number Theory - Henryk Iwaniec and Emmanuel Kowalski Un cours de théorie analytique des nombres - Emmanuel Kowalski Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics. The goal of this book is to present, in a motivated manner, the basic formalism of representation theory as well as some important applications. The style is intended to allow the reader to gain access to the insights and ideas of representation theory--not only to verify that a certain result is true, but also to explain why it is important and why the proof is natural. The presentation emphasizes the fact that the ideas of representation theory appear, sometimes in slightly different ways, in many contexts. Thus the book discusses in some detail the fundamental notions of representation theory for arbitrary groups. It then considers the special case of complex representations of finite groups and discusses the representations of compact groups, in both cases with some important applications. There is a short introduction to algebraic groups as well as an introduction to unitary representations of some noncompact groups. The text includes many exercises and examples. Readership Graduate students and research mathematicians interested in representation theory and its applications throughout mathematics. Table of Contents Introduction and motivation The language of representation theory Variants Linear representations of finite groups Abstract representation theory of compact groups Applications of representations of compact groups Other groups: a few examples Some useful facts Bibliography Index