Quotient Categories of Modular Representations -- Dipper–James–Murphy’s Conjecture for Hecke Algebras of Type Bn -- On Domino Insertion and Kazhdan–Lusztig Cells in Type Bn -- Runner Removal Morita Equivalences -- Quantum q-Schur Algebras and Their Infinite/Infinitesimal Counterparts -- Cherednik Algebras for Algebraic Curves -- A Temperley–Lieb Analogue for the BMW Algebra -- Graded Lie Algebras and Intersection Cohomology -- Crystal Base Elements of an ExtremalWeight Module Fixed by a Diagram Automorphism II: Case of Affine Lie Algebras -- t-Analogs of q-Characters of Quantum Affine Algebras of Type E6, E7, E8 -- Ultra-Discretization of the affine G_2 Geometric Crystals to Perfect Crystals -- On Hecke Algebras Associated with Elliptic Root Systems -- Green’s Formula with ?*-Action and Caldero–Keller’s Formula for Cluster Algebras.

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