Quantum Groups and Lie Theory

doi:10.1017/CBO9780511542848

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.

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

Source: EMS Newsletter

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Introduction
pp vii-viii
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Lectures on Cyclotomic Hecke Algebras
pp 1-22
- By Susumu Ariki
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An Introduction to Group Doublecross Products and Some Uses
pp 23-32
- By Edwin Beggs, Department of Mathematics University of Wales, Swansea Singleton Park, Swansea SA2 8PP, UK
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Canonical Bases and Piecewise-linear Combinatorics
pp 33-47
- By Roger Carter, Mathematics Institute, University of Warwick, Coventry CV4 7AL, England E-mail: rwc@maths.warwick.ac.uk, Robert Marsh, Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester LE1 7RH, England E-mail: R.Marsh@mcs.le.ac.uk
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Integrable and Weyl Modules for Quantum Affine sl2
pp 48-62
- By Vyjayanthi Chari, Andrew Pressley
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Notes on Balanced Categories and Hopf Algebras
pp 63-88
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Lectures on the dynamical Yang-Baxter Equations
pp 89-129
- By Pavel Etingof, Olivier Schiffmann
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Quantized Primitive Ideal Spaces as Quotients of Affine Algebraic Varietie
pp 130-148
- By K. R. Goodearl
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Representations of Semisimple Lie Algebras in Positive Characteristic and Quantum Groups at Roots of Unity
pp 149-167
- By Iain Gordon
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The Yang-Baxter Equation for Operators on Function Fields
pp 168-174
- By Jintai Ding, Timothy J. Hodges
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Noncommutative Differential Geometry and Twisting of Quantum Groups
pp 175-190
- By Shahn Majid, School of Mathematical Sciences, Queen Mary and Westfield College University of London, Mile End Rd, London E1 4NS
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Finite Quantum Groups and Pointed Hopf Algebras
pp 191-205
- By Ian M. Musson, Department of Mathematical Sciences University of Wisconsin-Milwaukee
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On Some Two Parameter Quantum and Jordanian Deformations, and their Coloured Extensions
pp 206-215
- By Deepak Parashar, Roger J. McDermott, School ofComputer and Mathematical Sciences The Robert Gordon University, St. Andrew Street Aberdeen AB25 1HG, United Kingdom
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Tensor Categories and Braid Representations
pp 216-234
- By Hans Wenzl
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Quantum Groups and Lie Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp vii-viii

Lectures on Cyclotomic Hecke Algebras
pp 1-22

An Introduction to Group Doublecross Products and Some Uses
pp 23-32

Canonical Bases and Piecewise-linear Combinatorics
pp 33-47

Integrable and Weyl Modules for Quantum Affine sl2
pp 48-62

Notes on Balanced Categories and Hopf Algebras
pp 63-88

Lectures on the dynamical Yang-Baxter Equations
pp 89-129

Quantized Primitive Ideal Spaces as Quotients of Affine Algebraic Varietie
pp 130-148

Representations of Semisimple Lie Algebras in Positive Characteristic and Quantum Groups at Roots of Unity
pp 149-167

The Yang-Baxter Equation for Operators on Function Fields
pp 168-174

Noncommutative Differential Geometry and Twisting of Quantum Groups
pp 175-190

Finite Quantum Groups and Pointed Hopf Algebras
pp 191-205

On Some Two Parameter Quantum and Jordanian Deformations, and their Coloured Extensions
pp 206-215

Tensor Categories and Braid Representations
pp 216-234

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Quantum Groups and Lie Theory

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