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Lie Groups

  • Daniel Bump

Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Compact Groups

    1. Front Matter
      Pages 1-1
    2. Daniel Bump
      Pages 3-5
    3. Daniel Bump
      Pages 6-16
    4. Daniel Bump
      Pages 17-20
    5. Daniel Bump
      Pages 21-26
  3. Lie Group Fundamentals

    1. Front Matter
      Pages 27-27
    2. Daniel Bump
      Pages 29-35
    3. Daniel Bump
      Pages 36-40
    4. Daniel Bump
      Pages 41-45
    5. Daniel Bump
      Pages 46-49
    6. Daniel Bump
      Pages 50-53
    7. Daniel Bump
      Pages 54-57
    8. Daniel Bump
      Pages 58-61
    9. Daniel Bump
      Pages 62-68
    10. Daniel Bump
      Pages 69-78
    11. Daniel Bump
      Pages 79-85
    12. Daniel Bump
      Pages 86-93
    13. Daniel Bump
      Pages 94-106
    14. Daniel Bump
      Pages 107-111
    15. Daniel Bump
      Pages 112-116
    16. Daniel Bump
      Pages 117-126
    17. Daniel Bump
      Pages 127-135
    18. Daniel Bump
      Pages 136-145
    19. Daniel Bump
      Pages 146-149
    20. Daniel Bump
      Pages 150-156
    21. Daniel Bump
      Pages 157-161
    22. Daniel Bump
      Pages 162-174
    23. Daniel Bump
      Pages 175-181
    24. Daniel Bump
      Pages 182-188
    25. Daniel Bump
      Pages 189-196
    26. Daniel Bump
      Pages 197-204
    27. Daniel Bump
      Pages 205-211
    28. Daniel Bump
      Pages 212-235
    29. Daniel Bump
      Pages 236-256
    30. Daniel Bump
      Pages 257-272
  4. Topics

    1. Front Matter
      Pages 273-273
    2. Daniel Bump
      Pages 275-283
    3. Daniel Bump
      Pages 284-288
    4. Daniel Bump
      Pages 289-296
    5. Daniel Bump
      Pages 297-307
    6. Daniel Bump
      Pages 308-314
    7. Daniel Bump
      Pages 315-320
    8. Daniel Bump
      Pages 321-330
    9. Daniel Bump
      Pages 331-338
    10. Daniel Bump
      Pages 339-346
    11. Daniel Bump
      Pages 347-356
    12. Daniel Bump
      Pages 357-360
    13. Daniel Bump
      Pages 361-369
    14. Daniel Bump
      Pages 370-374

About this book

Introduction

This book is intended for a one year graduate course on Lie groups and Lie algebras. The author proceeds beyond the representation theory of compact Lie groups (which is the basis of many texts) and provides a carefully chosen range of material to give the student the bigger picture. For compact Lie groups, the Peter-Weyl theorem, conjugacy of maximal tori (two proofs), Weyl character formula and more are covered. The book continues with the study of complex analytic groups, then general noncompact Lie groups, including the Coxeter presentation of the Weyl group, the Iwasawa and Bruhat decompositions, Cartan decomposition, symmetric spaces, Cayley transforms, relative root systems, Satake diagrams, extended Dynkin diagrams and a survey of the ways Lie groups may be embedded in one another. The book culminates in a ``topics'' section giving depth to the student's understanding of representation theory, taking the Frobenius-Schur duality between the representation theory of the symmetric group and the unitary groups as a unifying theme, with many applications in diverse areas such as random matrix theory, minors of Toeplitz matrices, symmetric algebra decompositions, Gelfand pairs, Hecke algebras, representations of finite general linear groups and the cohomology of Grassmannians and flag varieties.

Daniel Bump is Professor of Mathematics at Stanford University. His research is in automorphic forms, representation theory and number theory. He is a co-author of GNU Go, a computer program that plays the game of Go. His previous books include Automorphic Forms and Representations (Cambridge University Press 1997) and Algebraic Geometry (World Scientific 1998).

Keywords

Cohomology Fundamental group Matrix Matrix Theory Representation theory algebra homology

Authors and affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-4094-3
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1937-3
  • Online ISBN 978-1-4757-4094-3
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site