Algebraic groups and quantum groups : International Conference on Representation Theory of Algebraic Groups and Quantum Groups '10, August 2-6, 2010, Graduate School of Mathematics, Nagoya University, Nagoya, Japan / Susumu Ariki [and five others], editors.

Format:

Book

Conference/Event

Author/Creator:

International Conference on Representation Theory of Algebraic Groups and Quantum Groups, Corporate Author.

Contributor:

Ariki, Susumu, 1959- editor.

Conference Name:

International Conference on Representation Theory of Algebraic Groups and Quantum Groups (2010 : Nagoya-shi, Japan), issuing body.

International Conference on Representation Theory of Algebraic Groups and Quantum Groups

Series:

Contemporary mathematics (American Mathematical Society). 0271-4132 565

Contemporary mathematics, 565 0271-4132

Language:

English

Subjects (All):

Combinatorial group theory--Congresses.

Combinatorial group theory.

Representations of groups--Congresses.

Representations of groups.

Physical Description:

1 online resource (302 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2012]

Language Note:

English

Summary:

This volume contains the proceedings of the tenth international conference on Representation Theory of Algebraic Groups and Quantum Groups, held August 2-6, 2010, at Nagoya University, Nagoya, Japan. The survey articles and original papers contained in this volume offer a comprehensive view of current developments in the field. Among others reflecting recent trends, one central theme is research on representations in the affine case. In three articles, the authors study representations of W-algebras and affine Lie algebras at the critical level, and three other articles are related to crystals in the affine case, that is, Mirkovic-Vilonen polytopes for affine type $A$ and Kerov-Kirillov-Reshetikhin type bijection for affine type $E_6$. Other contributions cover a variety of topics such as modular representation theory of finite groups of Lie type, quantum queer super Lie algebras, Khovanov's arc algebra, Hecke algebras and cyclotomic $q$-Schur algebras, $G_1T$-Verma modules for reductive algebraic groups, equivariant $K$-theory of quantum vector bundles, and the cluster algebra. This book is suitable for graduate students and researchers interested in geometric and combinatorial representation theory, and other related fields.

Contents:

Preface

Program

W-algebras at the critical level

1. Introduction

2. Associated graded vertex Poisson algebras

3. BRST cohomology of restricted Wakimoto modules

4. Proof of Theorems 1.1 and 1.2

References

Highest weight modules at the critical level and noncommutative Springer resolution

2. Noncommutative Springer resolution

3. Perverse sheaves on the affine flag variety

4. Results of Frenkel-Gaitsgory and a proof of Theorem 1

An orthogonal form for level two Hecke algebras with applications

2. Level one Hecke algebras

3. Level two Hecke algebras

4. Khovanov's arc algebra

5. Category for Grassmannians

6. The general linear supergroup

7. The walled Brauer algebra

On the restricted projective objects in the affine category at the critical level

2. Affine Kac-Moody algebras

3. The deformed category

4. Projective objects in ̂_{ }

5. Block decomposition of ̂ _{ }

6. The linkage principle

Remarks on modular representations of finite groups of Lie type in non-defining characteristic

2. On modular unipotent representations

3. Principal series representations

4. On the dimensions of irreducible representations

Quantum queer superalgebras

Toward Berenstein-Zelevinsky data in affine type , Part I: Construction of the affine analogs

Toward Berenstein-Zelevinsky data in affine type , Part II: Explicit description

On tropical dualities in cluster algebras

KKR type bijection for the exceptional affine algebra ₆⁽¹⁾

Iwahori’s question for affine Hecke algebras

On Weyl modules of cyclotomic -Schur algebras

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

0-8218-8536-7