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A. Figá Talamanca: Random Fourier series on compact groups.- S. Helgason: Representations of semisimple Lie groups.- H. Jacquet: Représentations des groupes linéaires p-adiques.- G.W. Mackey: Infinite-dimensional group representations and their applications.
Representations of groups -- Congresses. --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Mathematics. --- Topological groups. --- Lie groups. --- Topological Groups, Lie Groups. --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Math --- Science --- Topological Groups.
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Ordered algebraic structures --- D-modules --- Quantum groups --- Representations of groups --- 51 --- Mathematics --- 51 Mathematics --- Congresses --- D-modules - Congresses. --- Global analysis (Mathematics) --- Analyse globale (mathématiques) --- Groupes quantiques. --- Algèbres non associatives --- Analyse microlocale --- K-théorie --- Quantum groups - Congresses. --- Representations of groups - Congresses. --- Algèbres non associatives --- Analyse globale (mathématiques) --- K-théorie
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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.
Group theory --- Representations of groups --- Finite groups --- Congresses --- Group theory. --- Associative rings. --- Rings (Algebra). --- Algebraic geometry. --- Group Theory and Generalizations. --- Associative Rings and Algebras. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Representations of groups - Congresses --- Finite groups - Congresses
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This volume contains invited articles by top-notch experts who focus on such topics as: modular representations of algebraic groups, representations of quantum groups and crystal bases, representations of affine Lie algebras, representations of affine Hecke algebras, modular or ordinary representations of finite reductive groups, and representations of complex reflection groups and associated Hecke algebras. Representation Theory of Algebraic Groups and Quantum Groups is intended for graduate students and researchers in representation theory, group theory, algebraic geometry, quantum theory and math physics. Contributors: H. H. Andersen, S. Ariki, C. Bonnafé, J. Chuang, J. Du, M. Finkelberg, Q. Fu, M. Geck, V. Ginzburg, A. Hida, L. Iancu, N. Jacon, T. Lam, G.I. Lehrer, G. Lusztig, H. Miyachi, S. Naito, H. Nakajima, T. Nakashima, D. Sagaki, Y. Saito, M. Shiota, J. Xiao, F. Xu, R. B. Zhang.
Lie groups -- Congresses. --- Quantum groups -- Congresses. --- Representations of groups -- Congresses. --- Lie groups --- Representations of groups --- Quantum groups --- Mathematics --- Physical Sciences & Mathematics --- Algebra --- Calculus --- Representations of algebras. --- Quantum groups. --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Mathematics. --- Algebraic geometry. --- Group theory. --- Nonassociative rings. --- Rings (Algebra). --- Topological groups. --- Lie groups. --- Number theory. --- Physics. --- Group Theory and Generalizations. --- Algebraic Geometry. --- Topological Groups, Lie Groups. --- Non-associative Rings and Algebras. --- Number Theory. --- Mathematical Methods in Physics. --- Group theory --- Mathematical physics --- Quantum field theory --- Geometry, algebraic. --- Topological Groups. --- Algebra. --- Mathematical physics. --- Groups, Topological --- Continuous groups --- Algebraic geometry --- Geometry --- Physical mathematics --- Physics --- Number study --- Numbers, Theory of --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups
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