Home » Representations Of Linear Groups: An Introduction Based On Examples From Physics And Number Theory by Rolf Berndt
Representations Of Linear Groups: An Introduction Based On Examples From Physics And Number Theory Rolf Berndt

Representations Of Linear Groups: An Introduction Based On Examples From Physics And Number Theory

Rolf Berndt

Published July 26th 2007
ISBN : 9783834803191
Paperback
271 pages
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 About the Book 

There are already many good books on representation theory for all kinds of groups. Two of the best (in this author s opinion) are the one by A.W. Knapp: Representation Theory for Semisimple Groups. An Overview based on Examples [Kn1] and by G.W.MoreThere are already many good books on representation theory for all kinds of groups. Two of the best (in this author s opinion) are the one by A.W. Knapp: Representation Theory for Semisimple Groups. An Overview based on Examples [Kn1] and by G.W. Mackey: Induced Representations in Physics, Probability and Number Theory [Ma1]. The title of this text is a mixture of both these titles, and our text is meant as a very elementary introduction to these and, moreover, to the whole topic of group repres- tations, even in?nite-dimensional ones. As is evident from the work of Bargmann [Ba], Weyl [Wey] and Wigner [Wi], group representations are fundamental for the theory of atomic spectra and elementary physics. But representation theory has proven to be an inavoidable ingredient in other ?elds as well, particularly in number theory, as in the theory of theta functions, automorphic forms, Galois representations and, ?nally, the Langlands program. Hence, we present an approach as elementary as possible, having in particular these applications in mind. This book is written as a summary of several courses given in Hamburg for students of Mathematics and Physics from the ?fth semester on. Thus, some knowledge of linear and multilinear algebra, calculus and analysis in several variables is taken for granted.