# Representation Theory

## A First Course

• William Fulton
• Joe Harris
Book

Part of the Graduate Texts in Mathematics book series (GTM, volume 129)

1. Front Matter
Pages i-xv
2. ### Finite Groups

1. Front Matter
Pages 1-2
2. William Fulton, Joe Harris
Pages 3-11
3. William Fulton, Joe Harris
Pages 12-25
4. William Fulton, Joe Harris
Pages 26-43
5. William Fulton, Joe Harris
Pages 44-62
6. William Fulton, Joe Harris
Pages 63-74
7. William Fulton, Joe Harris
Pages 75-88
3. ### Lie Groups and Lie Algebras

1. Front Matter
Pages 89-91
2. William Fulton, Joe Harris
Pages 93-103
3. William Fulton, Joe Harris
Pages 104-120
4. William Fulton, Joe Harris
Pages 121-132
5. William Fulton, Joe Harris
Pages 133-145
6. William Fulton, Joe Harris
Pages 146-160
7. William Fulton, Joe Harris
Pages 161-174
8. William Fulton, Joe Harris
Pages 175-193
4. ### The Classical Lie Algebras and Their Representations

1. Front Matter
Pages 195-195
2. William Fulton, Joe Harris
Pages 197-210
3. William Fulton, Joe Harris
Pages 211-237
4. William Fulton, Joe Harris
Pages 238-252

### Introduction

The primary goal of these lectures is to introduce a beginner to the finite­ dimensional representations of Lie groups and Lie algebras. Since this goal is shared by quite a few other books, we should explain in this Preface how our approach differs, although the potential reader can probably see this better by a quick browse through the book. Representation theory is simple to define: it is the study of the ways in which a given group may act on vector spaces. It is almost certainly unique, however, among such clearly delineated subjects, in the breadth of its interest to mathematicians. This is not surprising: group actions are ubiquitous in 20th century mathematics, and where the object on which a group acts is not a vector space, we have learned to replace it by one that is {e. g. , a cohomology group, tangent space, etc. }. As a consequence, many mathematicians other than specialists in the field {or even those who think they might want to be} come in contact with the subject in various ways. It is for such people that this text is designed. To put it another way, we intend this as a book for beginners to learn from and not as a reference. This idea essentially determines the choice of material covered here. As simple as is the definition of representation theory given above, it fragments considerably when we try to get more specific.

### Keywords

Abelian group algebra cohomology cohomology group finite group group action homology Lie algebra lie group representation theory Vector space

#### Authors and affiliations

• William Fulton
• 1
• Joe Harris
• 2
1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
2. 2.Department of MathematicsHarvard UniversityCambridgeUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-0979-9
• Copyright Information Springer Science+Business Media, Inc. 2004
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-3-540-00539-1
• Online ISBN 978-1-4612-0979-9
• Series Print ISSN 0072-5285
• Series Online ISSN 2197-5612