**Graduate Studies in Mathematics**

Volume: 155;
2014;
432 pp;
Hardcover

MSC: Primary 20; 22;

**Print ISBN: 978-1-4704-0966-1
Product Code: GSM/155**

List Price: $84.00

AMS Member Price: $67.20

MAA Member Price: $75.60

**Electronic ISBN: 978-1-4704-1857-1
Product Code: GSM/155.E**

List Price: $79.00

AMS Member Price: $63.20

MAA Member Price: $71.10

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# An Introduction to the Representation Theory of Groups

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*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.

#### Reviews & Endorsements

It is a good book: it's very useful and well-written. What with exercises scattered throughout, as well as examples and to-the-point remarks, it was clearly crafted with the student in mind.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## An Introduction to the Representation Theory of Groups

- Cover Cover11 free
- Title page iii4 free
- Contents v6 free
- Chapter 1. Introduction and motivation 18 free
- Chapter 2. The language of representation theory 1320 free
- Chapter 3. Variants 127134
- Chapter 4. Linear representations of finite groups 159166
- Chapter 5. Abstract representation theory of compact groups 269276
- Chapter 6. Applications of representations of compact groups 319326
- Chapter 7. Other groups: A few examples 355362
- Appendix A. Some useful facts 409416
- Bibliography 421428
- Index 425432 free
- Back Cover Back Cover1442