# Representation Theory of Algebraic Groups and Quantum Groups

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*Toshiaki Shoji; Masaki Kashiwara; Noriaki Kawanaka; George Lusztig; Ken-ichi Shinoda*

A publication of the Mathematical Society of Japan

This book is a collection of research and survey papers
written by speakers at the Mathematical Society of Japan's 10th
International Conference. It presents a comprehensive overview of
developments in representation theory of algebraic groups and quantum
groups. Particularly noteworthy are papers containing remarkable
results concerning Lusztig's conjecture on cells in affine Weyl
groups.

The following topics were discussed: cells in affine Weyl groups,
tilting modules, tensor categories attached to cells in affine Weyl
groups, representations of algebraic groups in positive
characteristic, representations of Hecke algebras, Ariki-Koike and
cyclotomic \(q\)-Schur algebras, cellular algebras and diagram algebras,
Gelfand-Graev representations of finite reductive groups, Green
functions associated to complex reflection groups, induction theorem
for Springer representations, representations of Lie algebras in
positive characteristic, representations of quantum affine algebras,
extremal weight modules, crystal bases, tropical
Robinson-Schensted-Knuth correspondence and more.

The material is suitable for graduate students and research
mathematicians interested in representation theory of algebraic
groups, Hecke algebras, quantum groups, and combinatorial
theory.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Volumes in this series are freely available electronically 5 years post-publication.

#### Readership

Graduate students and research mathematicians interested in algebra, algebraic geometry, mathematical physics, and combinatorial theory.