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Representation Theory of Finite Reductive Groups

Representation Theory of Finite Reductive Groups


Part of New Mathematical Monographs

  • Date Published: January 2004
  • availability: Available
  • format: Hardback
  • isbn: 9780521825177

£ 126.00

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About the Authors
  • At the crossroads of representation theory, algebraic geometry and finite group theory, this 2004 book blends together many of the main concerns of modern algebra, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of étale cohomology, leading to the proof of the recent Bonnafé–Rouquier theorems. The second is a straightforward and simplified account of the Dipper–James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors' version of Fong–Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.

    • Proofs of major and recent results in a very active field
    • Simplifications from published material that make possible the inclusion of those results in a single book
    • Emphasis on writing pedagogically with introductory chapters and appendices on background subjects
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    Reviews & endorsements

    'This monograph treats the representation theory of finite reductive groups mostly in transversal characteristic, i.e. in a characteristic that differs from the natural characteristic p of the group.' Zentralblatt MATH

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    Product details

    • Date Published: January 2004
    • format: Hardback
    • isbn: 9780521825177
    • length: 456 pages
    • dimensions: 229 x 152 x 29 mm
    • weight: 0.84kg
    • contains: 144 exercises
    • availability: Available
  • Table of Contents

    Notations and conventions
    Part I. Representing Finite BN-Pairs:
    1. Cuspidality in finite groups
    2. Finite BN-pairs
    3. Modular Hecke algebras for finite BN-pairs
    4. Modular duality functor and the derived category
    5. Local methods for the transversal characteristics
    6. Simple modules in the natural characteristic
    Part II. Deligne–Lusztig Varieties, Rational Series, and Morita Equivalences:
    7. Finite reductive groups and Deligne–Lusztig varieties
    8. Characters of finite reductive groups
    9. Blocks of finite reductive groups and rational series
    10. Jordan decomposition as a Morita equivalence, the main reductions
    11. Jordan decomposition as a Morita equivalence, sheaves
    12. Jordan decomposition as a Morita equivalence, modules
    Part III. Unipotent Characters and Unipotent Blocks:
    13. Levi subgroups and polynomial orders
    14. Unipotent characters as a basic set
    15. Jordan decomposition of characters
    16. On conjugacy classes in type D
    17. Standard isomorphisms for unipotent blocks
    Part IV. Decomposition Numbers and q-Schur Algebras:
    18. Some integral Hecke algebras
    19. Decomposition numbers and q-Schur algebras, general linear groups
    20. Decomposition numbers and q-Schur algebras, linear primes
    Part V. Unipotent Blocks and Twisted Induction:
    21. Local methods. Twisted induction for blocks
    22. Unipotent blocks and generalized Harish Chandra theory
    23. Local structure and ring structure of unipotent blocks
    Appendix 1: Derived categories and derived functors
    Appendix 2: Varieties and schemes
    Appendix 3: Etale cohomology

  • Authors

    Marc Cabanes, Université de Paris VII (Denis Diderot)

    Michel Enguehard, Université de Paris VII (Denis Diderot)

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