Book contents
- Frontmatter
- Contents
- Preface
- 1 Finite Groups of Lie Type
- 2 Simple Modules
- 3 Weyl Modules and Lusztig's Conjecture
- 4 Computation of Weight Multiplicities
- 5 Other Aspects of Simple Modules
- 6 Tensor Products
- 7 BN-Pairs and Induced Modules
- 8 Blocks
- 9 Projective Modules
- 10 Comparison with Frobenius Kernels
- 11 Cartan Invariants
- 12 Extensions of Simple Modules
- 13 Loewy Series
- 14 Cohomology
- 15 Complexity and Support Varieties
- 16 Ordinary and Modular Representations
- 17 Deligne–Lusztig Characters
- 18 The Groups G2(q)
- 19 General and Special Linear Groups
- 20 Suzuki and Ree Groups
- Bibliography
- Frequently Used Symbols
- Index
Preface
Published online by Cambridge University Press: 23 November 2009
- Frontmatter
- Contents
- Preface
- 1 Finite Groups of Lie Type
- 2 Simple Modules
- 3 Weyl Modules and Lusztig's Conjecture
- 4 Computation of Weight Multiplicities
- 5 Other Aspects of Simple Modules
- 6 Tensor Products
- 7 BN-Pairs and Induced Modules
- 8 Blocks
- 9 Projective Modules
- 10 Comparison with Frobenius Kernels
- 11 Cartan Invariants
- 12 Extensions of Simple Modules
- 13 Loewy Series
- 14 Cohomology
- 15 Complexity and Support Varieties
- 16 Ordinary and Modular Representations
- 17 Deligne–Lusztig Characters
- 18 The Groups G2(q)
- 19 General and Special Linear Groups
- 20 Suzuki and Ree Groups
- Bibliography
- Frequently Used Symbols
- Index
Summary
“I confess I like to take account of possibilities. Don't you know mathematics are my hobby? Did you ever study algebra? I always have an eye on the unknown quantity”.
Henry James, The Story of a YearIch predige die Mathematik … … Die Beschäftigung mit der Mathematik, sage ich, ist das beste Mittel gegen die Kupiditäat. Staatsanwalt Paravant, der stark angefochten war, hat sich drauf geworfen, er hat es jetzt mit der Quadratur des Kreises und spürt große Erleichterung.
Thomas Mann, Der Zauberberg– Ah! c'etait impossible, les cours duraient parfois fort tard.
– Même après 2 heures du matin? demandait le baron.
– Des fois.
– Mais l'algèbre s'apprend aussi facilement dans un livre.
– Même plus facilement, car je ne comprends pas grand' chose aux cours.
– Alors? D'ailleurs l'algèbre ne peut te servir à rien.
– J'aime bien cela. Ca dissipe ma neurasthénie.
Marcel Proust, Sodome et GomorrheWhatever its therapeutic value may be, group theory offers plenty of diversions and challenges. In particular, the study of finite groups of Lie type and their representations (ordinary or modular) leads to deep questions, many of which are still unsolved.
A more accurate but cumbersome title for this book would be: “A guide to the modular representation theory of finite groups of Lie type in the defining characteristic p”. As a subtheme, the relationship between ordinary and modular representations is explored, in the context of Deligne–Lusztig characters.
- Type
- Chapter
- Information
- Modular Representations of Finite Groups of Lie Type , pp. xiii - xviPublisher: Cambridge University PressPrint publication year: 2005