**Contemporary Mathematics**

Volume: 433;
2007;
336 pp;
Softcover

MSC: Primary 16; 81; 18; 17;

Print ISBN: 978-0-8218-3713-9

Product Code: CONM/433

List Price: $105.00

Individual Member Price: $84.00

**Electronic ISBN: 978-0-8218-8112-5
Product Code: CONM/433.E**

List Price: $105.00

Individual Member Price: $84.00

# Quantum Groups

Share this page *Edited by *
*Pavel Etingof; Shlomo Gelaki; Steven Shnider*

A co-publication of the AMS and Bar-Ilan University

The papers in this volume are based on the talks given at the conference on
quantum groups dedicated to the memory of Joseph Donin, which was held
at the Technion Institute, Haifa, Israel in July 2004. A survey of
Donin's distinguished mathematical career is included. Several
articles, which were directly influenced by the research of Donin and
his colleagues, deal with invariant quantization, dynamical
\(R\)-matrices, Poisson homogeneous spaces, and reflection
equation algebras. The topics of other articles include Hecke
symmetries, orbifolds, set-theoretic solutions to the pentagon
equations, representations of quantum current algebras, unipotent
crystals, the Springer resolution, the Fourier transform on Hopf
algebras, and, as a change of pace, the combinatorics of smoothly
knotted surfaces.

The articles all contain important new contributions to their respective
areas and will be of great interest to graduate students and research
mathematicians interested in Hopf algebras, quantum groups, and
applications.

#### Table of Contents

# Table of Contents

## Quantum Groups

- Contents v6 free
- Preface vii8 free
- Conference program ix10 free
- List of participants xiii14 free
- Joseph Donin's mathematical research, 1966–2003 116 free
- Geometric and unipotent crystals II: From unipotent bicrystals to crystal bases 1328
- The small quantum group and the Springer resolution 89104
- Relation between two geometrically defined bases in representations of G Ln 103118
- Fourier transforms for Hopf algebras 115130
- Quantization of some Poisson-Lie dynamical r-matrices and Poisson homogeneous spaces 135150
- Basic representations of quantum current algebras in higher genus 177192
- Poincaré-Birkhoff-Witt expansions of the canonical elliptic differential form 191206
- Geometry of non-commutative orbits related to Hecke symmetries 209224
- Drinfeld double for orbifolds 251266
- Symmetrically factorizable groups and set-theoretical solutions of the pentagon equation 267282
- Dynamical reflection equation 281296
- On the combinatorics of Carter-Rieger-Saito movies in the theory of smoothly knotted surfaces in R4 311326

#### Readership

Graduate students and research mathematicians interested in Hopf algebras, quantum groups, and applications.