Representation theory of algebraic groups and quantum groups

✍ Scribed by Henning Haahr Andersen (auth.), Akihiko Gyoja, Hiraku Nakajima, Ken-ichi Shinoda, Toshiaki Shoji, Toshiyuki Tanisaki (eds.)

• Publisher: Birkhäuser Basel
• Year: 2010
• Tongue: English
• Leaves: 363
• Series: Progress in Mathematics 284
• Edition: 1
• Category: Library

✦ Synopsis

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

✦ Table of Contents

Front Matter....Pages i-xiii
Quotient Categories of Modular Representations....Pages 1-16
Dipper–James–Murphy’s Conjecture for Hecke Algebras of Type B n ....Pages 17-32
On Domino Insertion and Kazhdan–Lusztig Cells in Type B n ....Pages 33-54
Runner Removal Morita Equivalences....Pages 55-92
Quantum $$\mathfrak{gl}_n,$$ q -Schur Algebras and Their Infinite/Infinitesimal Counterparts....Pages 93-119
Cherednik Algebras for Algebraic Curves....Pages 121-153
A Temperley–Lieb Analogue for the BMW Algebra....Pages 155-190
Graded Lie Algebras and Intersection Cohomology....Pages 191-224
Crystal Base Elements of an ExtremalWeight Module Fixed by a Diagram Automorphism II: Case of Affine Lie Algebras....Pages 225-255
t -Analogs of q -Characters of Quantum Affine Algebras of Type E6, E7, E8....Pages 257-272
Ultra-Discretization of the affine G_2 Geometric Crystals to Perfect Crystals....Pages 273-296
On Hecke Algebras Associated with Elliptic Root Systems....Pages 297-312
Green’s Formula with ℂ * -Action and Caldero–Keller’s Formula for Cluster Algebras....Pages 313-348

✦ Subjects

Group Theory and Generalizations;Algebraic Geometry;Topological Groups, Lie Groups;Non-associative Rings and Algebras;Number Theory;Mathematical Methods in Physics