Ebook: Finite Reductive Groups: Related Structures and Representations: Proceedings of an International Conference held in Luminy, France
- Tags: Group Theory and Generalizations, Associative Rings and Algebras, Algebraic Geometry
- Series: Progress in Mathematics 141
- Year: 1996
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
Finite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the subject was revolutionized by the introduction of constructions from l-adic cohomology by Deligne-Lusztig (1976) and by the approach of character-sheaves by Lusztig (1985). The theory now also incorporates the methods of Brauer for the linear representations of finite groups in arbitrary characteristic and the methods of representations of algebras. It has become one of the most active fields of contemporary mathematics.
The present volume reflects the richness of the work of experts gathered at an international conference held in Luminy. Linear representations of finite reductive groups (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular aspects Cabanes Enguehard, Geck-Hiss) go side by side with many related structures: Hecke algebras associated with Coxeter groups (Ariki, Geck-Rouquier, Pfeiffer), complex reflection groups (Broué-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vignéras), Lie groups (Cohen-Tiep), symmetric groups (Bessenrodt-Olsson), and general finite groups (Puig). With the illuminating introduction by Paul Fong, the present volume forms the best invitation to the field.
Finite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the subject was revolutionized by the introduction of constructions from l-adic cohomology by Deligne-Lusztig (1976) and by the approach of character-sheaves by Lusztig (1985). The theory now also incorporates the methods of Brauer for the linear representations of finite groups in arbitrary characteristic and the methods of representations of algebras. It has become one of the most active fields of contemporary mathematics.
The present volume reflects the richness of the work of experts gathered at an international conference held in Luminy. Linear representations of finite reductive groups (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular aspects Cabanes Enguehard, Geck-Hiss) go side by side with many related structures: Hecke algebras associated with Coxeter groups (Ariki, Geck-Rouquier, Pfeiffer), complex reflection groups (Brou?-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vign?ras), Lie groups (Cohen-Tiep), symmetric groups (Bessenrodt-Olsson), and general finite groups (Puig). With the illuminating introduction by Paul Fong, the present volume forms the best invitation to the field.
Finite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the subject was revolutionized by the introduction of constructions from l-adic cohomology by Deligne-Lusztig (1976) and by the approach of character-sheaves by Lusztig (1985). The theory now also incorporates the methods of Brauer for the linear representations of finite groups in arbitrary characteristic and the methods of representations of algebras. It has become one of the most active fields of contemporary mathematics.
The present volume reflects the richness of the work of experts gathered at an international conference held in Luminy. Linear representations of finite reductive groups (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular aspects Cabanes Enguehard, Geck-Hiss) go side by side with many related structures: Hecke algebras associated with Coxeter groups (Ariki, Geck-Rouquier, Pfeiffer), complex reflection groups (Brou?-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vign?ras), Lie groups (Cohen-Tiep), symmetric groups (Bessenrodt-Olsson), and general finite groups (Puig). With the illuminating introduction by Paul Fong, the present volume forms the best invitation to the field.
Content:
Front Matter....Pages i-xii
q-Analogue of a Twisted Group Ring....Pages 1-13
Formule des traces sur les corps finis....Pages 15-49
Heights of Spin Characters in Characteristic 2....Pages 51-71
Sur certains ?l?ments r?guliers des groupes de Weyl et les vari?t?s de Deligne—Lusztig associ?es....Pages 73-139
Local Methods for Blocks of Reductive Groups over a Finite Field....Pages 141-163
Splitting Fields for Jordan Subgroups....Pages 165-183
A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations....Pages 185-194
Modular Representations of Finite Groups of Lie Type in Non-defining Characteristic....Pages 195-249
Centers and Simple Modules for Iwahori-Hecke Algebras....Pages 251-272
Quantum Groups, Hall Algebras and Quantized Shuffles....Pages 273-290
Fourier transforms, Nilpotent Orbits, Hall Polynomials and Green Functions....Pages 291-309
Degr?s relatifs des alg?bres cyclotomiques associ?es aux groupes de r?flexions complexes de dimension deux....Pages 311-332
Character Values of Iwahori—Hecke Algebras of Type B....Pages 333-360
The Center of a Block....Pages 361-372
Unipotent Characters of Finite Classical Groups....Pages 373-413
A propos d’une conjecture de Langlands modulaire....Pages 415-452
Finite reductive groups and their representations lie at the heart of goup theory. After representations of finite general linear groups were determined by Green (1955), the subject was revolutionized by the introduction of constructions from l-adic cohomology by Deligne-Lusztig (1976) and by the approach of character-sheaves by Lusztig (1985). The theory now also incorporates the methods of Brauer for the linear representations of finite groups in arbitrary characteristic and the methods of representations of algebras. It has become one of the most active fields of contemporary mathematics.
The present volume reflects the richness of the work of experts gathered at an international conference held in Luminy. Linear representations of finite reductive groups (Aubert, Curtis-Shoji, Lehrer, Shoji) and their modular aspects Cabanes Enguehard, Geck-Hiss) go side by side with many related structures: Hecke algebras associated with Coxeter groups (Ariki, Geck-Rouquier, Pfeiffer), complex reflection groups (Brou?-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vign?ras), Lie groups (Cohen-Tiep), symmetric groups (Bessenrodt-Olsson), and general finite groups (Puig). With the illuminating introduction by Paul Fong, the present volume forms the best invitation to the field.
Content:
Front Matter....Pages i-xii
q-Analogue of a Twisted Group Ring....Pages 1-13
Formule des traces sur les corps finis....Pages 15-49
Heights of Spin Characters in Characteristic 2....Pages 51-71
Sur certains ?l?ments r?guliers des groupes de Weyl et les vari?t?s de Deligne—Lusztig associ?es....Pages 73-139
Local Methods for Blocks of Reductive Groups over a Finite Field....Pages 141-163
Splitting Fields for Jordan Subgroups....Pages 165-183
A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations....Pages 185-194
Modular Representations of Finite Groups of Lie Type in Non-defining Characteristic....Pages 195-249
Centers and Simple Modules for Iwahori-Hecke Algebras....Pages 251-272
Quantum Groups, Hall Algebras and Quantized Shuffles....Pages 273-290
Fourier transforms, Nilpotent Orbits, Hall Polynomials and Green Functions....Pages 291-309
Degr?s relatifs des alg?bres cyclotomiques associ?es aux groupes de r?flexions complexes de dimension deux....Pages 311-332
Character Values of Iwahori—Hecke Algebras of Type B....Pages 333-360
The Center of a Block....Pages 361-372
Unipotent Characters of Finite Classical Groups....Pages 373-413
A propos d’une conjecture de Langlands modulaire....Pages 415-452
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