**Contemporary Mathematics**

Volume: 413;
2006;
254 pp;
Softcover

MSC: Primary 05; 14; 16; 17; 20;

**Print ISBN: 978-0-8218-3924-9
Product Code: CONM/413**

List Price: $92.00

AMS Member Price: $73.60

MAA Member Price: $82.80

**Electronic ISBN: 978-0-8218-8088-3
Product Code: CONM/413.E**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

# Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

Share this page *Edited by *
*Georgia Benkart; Jens C. Jantzen; Zongzhu Lin; Daniel K. Nakano; Brian J. Parshall*

The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.

#### Readership

Graduate students and research mathematicians interested in various aspects of representation theory.

# Table of Contents

## Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

- Contents v6 free
- Preface vii8 free
- List of Talks ix10 free
- List of Participants xi12 free
- Extensions for finite groups of Lie type II: Filtering the truncated induction functor 114 free
- Algebras, representations and their derived categories over finite fields 2538
- On localization of D-modules 4356
- Representations of reduced enveloping algebras and cells in the affine Weyl group 6376
- Nakajima's monomials and crystal bases 7386
- A new Lie bialgebra structure on sl(2, 1) 101114
- The Steinberg tensor product theorem for GL(m|n) 123136
- Cyclotomic q-Schur algebras and Schur-Weyl duality 133146
- Geometric crystals and affine crystals 157170
- Self-extensions for finite symplectic groups via algebraic groups 173186
- Classification of finite dimensional simple Lie algebras in prime characteristics 185198
- From quantum groups to unitary modular tensor categories 215228
- A trip from representations of the Kronecker quiver to canonical bases of quantum affine algebras 231244