Readings in Mathematics

Representation Theory

A First Course

Authors: Fulton, William, Harris, Joe

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About this Textbook

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.

Table of contents (26 chapters)

  • Representations of Finite Groups

    Fulton, William (et al.)

    Pages 3-11

  • Characters

    Fulton, William (et al.)

    Pages 12-25

  • Examples; Induced Representations; Group Algebras; Real Representations

    Fulton, William (et al.)

    Pages 26-43

  • Representations of $${\mathfrak{S}_{_d}}$$ : Young Diagrams and Frobenius’s Character Formula

    Fulton, William (et al.)

    Pages 44-62

  • Representations of $${\mathfrak{U}_d}$$ and $$G{L_2}\left( {{\mathbb{F}_q}} \right)$$

    Fulton, William (et al.)

    Pages 63-74

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-1-4612-0979-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-0-387-97495-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Representation Theory
Book Subtitle
A First Course
Authors
Series Title
Readings in Mathematics
Series Volume
129
Copyright
2004
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0979-9
DOI
10.1007/978-1-4612-0979-9
Softcover ISBN
978-0-387-97495-8
Edition Number
1
Number of Pages
XV, 551
Topics