Group Representation Theory

Preface
Representations, Functors and Cohomology
Cohomology and Representation Theory
Jon F. Carlson
1. Introduction
2. Modules over p-groups
3. Group cohomology
4. Support varieties
5. The cohomology ring of a dihedral group
6. Elementary abelian subgroups in cohomology and representations
7. Quillen's dimension theorem
8. Properties of support varieties
9. The rank of the group of endotrivial modules
Introduction to Block Theory
Radha Kessar
1. Introduction
2. Brauer pairs
3. b-Brauer pairs
4. Some structure theory
5. Alperin's weight conjecture
6. Blocks in characteristic
7. Examples of fusion systems
Introduction to Fusion Systems
Markus Linckelmann
1. Local structure of finite groups
2. Fusion systems
3. Normalisers and centralisers
4. Centric subgroups
5. Alperin's fusion theorem
6. Quotients of fusion systems
7. Normal fusion systems
8. Simple fusion systems
9. Normal subsystems and control of fusion
Endo-permutation Modules, a Guided Tour
Jacques Th'evenaz
1. Introduction
2. Endo-permutation modules
3. The Dade group
4. Examples
5. The abelian case
6. Some small groups
7. Detection of endo-trivial modules
8. Classification of endo-trivial modules
9. Detection of endo-permutation modules
10. Functorial approach
11. The dual Burnside ring
12. Rational representations and an induction theorem
13. Classification of endo-permutation modules
14. Consequences of the classification
An Introduction to the Representations and Cohomology of Categories
Peter Webb
1. Introduction
2. The category algebra and some preliminaries
3. Restriction and induction of representations
4. Parametrization of simple and projective representations
5. The constant functor and limits
6. Augmentation ideals, derivations and H1
7. Extensions of categories and H2
Algebraic Groups and Finite Reductive Groups
An Algebraic Introduction to Complex Reflection Groups
Michel Brou'e
Part I. Commutative Algebra: a Crash Course
1. Notations, conventions, and prerequisites
2. Graded algebras and modules
3. Filtrations: associated graded algebras, completion
4. Finite ring extensions
5. Local or graded k-rings
6. Free resolutions and homological dimension
7. Regular sequences, Koszul complex, depth
Part II. Reflection Groups
8. Reflections and roots
9. Finite group actions on regular rings
10. Ramification and reflecting pairs
11. Characterization of reflection groups
12. Generalized characteristic degrees and Steinberg theorem
13. On the co-invariant algebra
14. Isotypic components of the symmetric algebra
15. Differential operators, harmonic polynomials
16. Orlik-Solomon theorem and first applications
17. Eigenspaces
Representations of Algebraic Groups
Stephen Donkin
1. Algebraic groups and representations
2. Representations of semisimple groups
3. Truncation to a Levi subgroup
Modular Representations of Hecke Algebras
Meinolf Geck
1. Introduction
2. Harish-Chandra series and Hecke algebras
3. Unipotent blocks
4. Generic Iwahori-Hecke algebras and specializations
5. The Kazhdan-Lusztig basis and the a-function
6. Canonical basic sets and Lusztig's ring J
7. The Fock space and canonical bases
8. The theorems of Ariki and Jacon
Topics in the Theory of Algebraic Groups
Gary M. Seitz
1. Introduction
2. Algebraic groups: introduction
3. Morphisms of algebraic groups
4. Maximal subgroups of classical algebraic groups
5. Maximal subgroups of exceptional algebraic groups
6. On the finiteness of double coset spaces
7. Unipotent elements in classical groups
8. Unipotent classes in exceptional groups
Bounds for the Orders of the Finite Subgroups of G(k)
Jean-Pierre Serre
Lecture I. History: Minkowski, Schur
1. Minkowski
2. Schur
3. Blichfeldt and others
Lecture II. Upper Bounds
4. The invariants t and m
5. The S-bound
6. The M-bound
Lecture III. Construction of large subgroups
7. Statements
8. Arithmetic methods (k = Q)
9. Proof of theorem 9 for classical groups
10. Galois twists
11. A general construction
12. Proof of theorem 9 for exceptional groups
13. Proof of theorems 10 and 11
14. The case m = 1
Index