Representation Theory of Algebraic Groups and Quantum Groups

Representation Theory of Algebraic Groups and Quantum Groups

by Toshiaki Shoji, Ken-ichi Shinoda, George Lusztig, Noriaki Kawanaka
     
 

ISBN-10: 4931469256

ISBN-13: 9784931469259

Pub. Date: 07/10/2004

Publisher: 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

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Overview

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.

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Product Details

ISBN-13:
9784931469259
Publisher:
Mathematical Society of Japan
Publication date:
07/10/2004
Series:
Advanced Studies in Pure Mathematics Series, #40
Pages:
512
Product dimensions:
(w) x (h) x 1.18(d)

Related Subjects

Table of Contents

Cells in affine Weyl groups and tilting modules1
Heche algebras with a finite number of indecomposable modules17
Algebraic construction of contragradient quasi-Verma modules in positive characteristic27
On tensor categories attached to cells in affine Weyl groups69
AppBraiding compatibilities91
On tensor categories attached to cells in affine Weyl groups II101
Zeta functions and functional equations associated with the components of the Gelfand-Graev representations of a finite reductive group121
Cellular algebras and diagram algebras in representation theory141
Representations of lie algebras in positive characteristic175
Quantum affine algebras and crystal bases219
An induction theorem for Springer's representations253
The representation theory of the Ariki-Koike and cyclotomic q- Schur algebras261
Crystal bases and diagram automorphisms321
Extremal weight modules of quantum affine algebras343
Tropical Robinson-Schensted-Knuth correspondence and birational Weyl group actions371
Green functions attached to limit symbols443
Cells for a Hecke algebra representation469
On the characterization of the set D[subscript 1] of the affine Weyl group of type [actual symbol not reproducible][subscript n]483

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