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TitleFinite Reductive Groups: Related Structures and Representations [electronic resource] : Proceedings of an International Conference held in Luminy, France / edited by Marc Cabanes
ImprintBoston, MA : Birkhรคuser Boston, 1997
Connect tohttp://dx.doi.org/10.1007/978-1-4612-4124-9
Descript XII, 452 p. online resource

SUMMARY

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 (Brouรฉ-Michel, Malle), quantum groups and Hall algebras (Green), arithmetic groups (Vignรฉras), 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

q-Analogue of a Twisted Group Ring -- Formule des traces sur les corps finis -- Heights of Spin Characters in Characteristic 2 -- Sur certains รฉlรฉments rรฉguliers des groupes de Weyl et les variรฉtรฉs de Deligne-Lusztig associรฉes -- Local Methods for Blocks of Reductive Groups over a Finite Field -- Splitting Fields for Jordan Subgroups -- A Norm Map for Endomorphism Algebras of Gelfand-Graev Representations -- Modular Representations of Finite Groups of Lie Type in Non-Defining Characteristic -- Centers and Simple Modules for Iwahori-Hecke Algebras -- Quantum Groups, Hall Algebras and Quantized Shuffles -- Fourier Transforms, Nilpotent Orbits, Hall Polynomials and Green Functions -- Degrรฉs relatifs des algรจbres cyclotomiques associรฉes aux groupes de rรฉflexions complexes de dimension deux -- Character Values of Iwahori-Hecke Algebras of Type B -- The Center of a Block -- Unipotent Characters of Finite Classical Groups -- A propos dโ{128}{153}une conjecture de Langlands modulaire


Mathematics Algebraic geometry Associative rings Rings (Algebra) Group theory Mathematics Group Theory and Generalizations Associative Rings and Algebras Algebraic Geometry



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