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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