Quantum Groups and Lie Theory

by Andrew Pressley

Overview

To take stock and to discuss the most fruitful directions for future research, many of the world's leading figures 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.

Product Details

ISBN-13:	9780521010405
Publisher:	Cambridge University Press
Publication date:	01/17/2002
Series:	London Mathematical Society Lecture Note Series , #290
Pages:	242
Product dimensions:	5.98(w) x 8.98(h) x 0.59(d)

Table of Contents

Introduction; 1. Lectures on cyclotomic Hecke algebras Susumu Ariki; 2. An introduction to group doublecross products and some uses Edwin Beggs; 3. Canonical bases and piecewise-linear combinatorics Roger Carter and Robert Marsh; 4. Integrable and Weyl modules for quantum affine sl2 Vyjayanthi Chari and Andrew Pressley; 5. Notes on balanced categories and Hopf algebras Bernhard Drabant; 6. Lectures on the dynamical Yang-Baxter equations Pavel Etingof and Olivier Schiffmann; 7. Quantized primitive ideal spaces as quotients of affine algebraic varieties K. R. Goodearl; 8. Representations of semisimple Lie algebras in positive characteristic and quantum groups at roots of unity Iain Gordon; 9. The Yang-Baxter equation for operators on function fields Jintai Ding and Timothy J. Hodges; 10. Noncommutative differential geometry and twisting of quantum groups Shahn Majid; 11. Finite quantum group and pointed Hopf algebras Ian M. Musson; 12. On some two parameter quantum and Jordanian deformations, and their coloured extensions Deepak Parashar and Roger J. McDermott; 13. Tensor categories and braid representations Hans Wenzl.

Editorial Reviews

'… an interesting collection of papers in the field.' EMS Newsletter

From the Publisher