Quantum Groups and Lie Theory

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  • Format: Paperback
  • Copyright: 2002-02-25
  • Publisher: Cambridge University Press
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Since its genesis in the early 1980s, the subject of quantum groups has grown rapidly. By the late 1990s most of the foundational issues had been resolved and many of the outstanding problems clearly formulated. To take stock and to discuss the most fruitful directions for future research many of the world's leading figures in this area met at the Durham Symposium on Quantum Groups in the summer of 1999, and this volume provides an excellent overview of the material presented there. It includes important surveys of both cyclotomic Hecke algebras and the dynamical Yang-Baxter equation. Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.

Table of Contents

Introduction vii
Lectures on Cyclotomic Hecke Algebras
Susumu Ariki
An Introduction to Group Doublecross Products and Some Uses
Edwin Beggs
Canonical Bases and Piecewise-linear Combinatorics
Roger Carter
Robert Marsh
Integrable and Weyl Modules for Quantum Affine sl2
Vyjayanthi Chari
Andrew Pressley
Notes on Balanced Categories and Hopf Algebras
Bernhard Drabant
Lectures on the Dynamical Yang-Baxter Equations
Pavel Etinhof
Olivier Schiffmann
Quantized Primitive Ideal Spaces as Quotients of Affine Algebraic Varieties
K. R. Goodearl
Representations of Semisimple Lie Algebras in Positive Characteristic and Quantum Groups at Roots of Unity
Iain Gordon
The Yang-Baxter Equation for Operators on Function Fields
Jintai Ding
Timothy J. Hodges
Noncommutative Differential Geometry and Twisting of Quantum Groups
Shahn Majid
Finite Quantum Groups and Pointed Hopf Algebras
Ian M. Musson
On Some Two Parameter Quantum and Jordanian Deformations, and their Coloured Extensions
Deepak Parashar
Roger J. McDermott
Tensor Categories and Braid Representations
Hans Wenzl

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