Representation Theory

A First Course

  • William Fulton
  • Joe Harris

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

Table of contents

  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 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 211-237
    3. William Fulton, Joe Harris
      Pages 238-252

About this book


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.


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
  • Copyright Information Springer Science+Business Media, Inc. 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-00539-1
  • Online ISBN 978-1-4612-0979-9
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • About this book