Contains articles by many of the participants at the conference on modular representation theory of finite groups, which took place under the auspices of the Mathematical Research Institute of the Ohio State University with additional support from the National Science Foundation. The book is addressed to specialists and students in the field of group representation theory, including both the general theory and the special theories related to the representations of the symmetric groups and the finite groups of Lie type. Latest reports are given on important conjectures including the Lusztig conjecture, the Alperin-McKay-Dade conjectures and the k(GV) problem. Important new research avenues are illuminated, including the theory of infinite-dimensional modules for finite groups and the theory of Rickard equivalences of module categories.
Author(s): Ronald Solomon
Series: Ohio State University Mathematical Research Institute Publications, 6
Publisher: Walter de Gruyter
Year: 1997
Language: English
Pages: 156
Representation Theory of Finite Groups......Page 1
Preface......Page 6
Table of Contents......Page 9
Introduction......Page 11
Geometries......Page 12
Sheaf Theory......Page 13
Embeddings......Page 15
Conclusion......Page 16
Bibliography......Page 18
1. A Vector Space Lemma......Page 20
2. Dade's Lemma......Page 21
4. Generic Points......Page 23
5. Properties of VrE(M)......Page 24
6. An Example......Page 25
References......Page 26
H. I. Blau: Degrees and Diagrams of Integral Table Algebras......Page 27
1. Introduction and Preliminaries......Page 36
2. The Canonical Brauer Induction Formula......Page 40
3. Variations of the Canonical Brauer Induction Formula......Page 43
4. Projectification......Page 44
5. Projectification and the Defect of an Irreducible Character......Page 48
References......Page 49
1. The Basic Conjecture......Page 52
2. The Invariant Conjecture......Page 54
3. The Extended Conjecture......Page 56
4. Projective Conjectures......Page 57
5. The Inductive Conjecture......Page 60
6. Simple G......Page 65
References......Page 66
H. Ellers: The Defect Groups of a Clique......Page 67
1. Symmetric Groups Sr and Schur Algebras......Page 73
2. GLn(K)-Modules and Tilting Modules......Page 75
3. Symmetric Groups and Schur Algebras......Page 78
4. Decomposition Numbers......Page 81
5. Dimensions of Simple Modules for Symmetric Groups......Page 83
References......Page 89
1. Introduction......Page 91
2. Strong Covering and its Characterizations......Page 92
3. Brauer's Third Main Theorem under Extended Induction......Page 94
4. A Class of Infinitely Many Counterexamples to the Transitivity of Extended Induction......Page 95
References......Page 96
1. Source Algebras, Their Definitions and Some Properties......Page 98
2. Puig's Conjecture......Page 100
References......Page 104
1. Introduction......Page 106
2. The Noninjective Induction......Page 108
3. Morita Equivalences between Brauer Blocks......Page 112
4. The Differential Structures......Page 116
5. Rickard Equivalences between Brauer Blocks......Page 121
6. Basic Rickard Equivalences between Brauer Blocks......Page 125
References......Page 130
The "k(B) at most p^d" Conjecture......Page 132
Conjectures of Alperin-Dade Type......Page 134
References......Page 135
L. L. Scott: Are All Groups Finite?......Page 137
1.1 Highest weight categories, and examples......Page 139
Three examples in Lie theory......Page 140
1.2 Quasihereditary algebras......Page 143
1.4 Stratified algebras......Page 145
References......Page 150
S. A. Syskin: Locally Finite Varieties of Groups and Representations of Finite Groups......Page 153
Back Cover......Page 156
