**Contemporary Mathematics**

Volume: 297;
2002;
334 pp;
Softcover

MSC: Primary 17;
Secondary 81; 82

Print ISBN: 978-0-8218-2716-1

Product Code: CONM/297

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

**Electronic ISBN: 978-0-8218-7887-3
Product Code: CONM/297.E**

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

# Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

Share this page *Edited by *
*Stephen Berman; Paul Fendley; Yi-Zhi Huang; Kailash Misra; Brian Parshall*

Because of its many applications to mathematics and mathematical physics, the
representation theory of infinite-dimensional Lie and quantized enveloping
algebras comprises an important area of current research. This volume includes
articles from the proceedings of an international conference, “Infinite-Dimensional Lie Theory and Conformal Field Theory”, held at the University
of Virginia. Many of the contributors to the volume are prominent researchers
in the field.

This conference provided an opportunity for mathematicians and physicists to
interact in an active research area of mutual interest. The talks focused on
recent developments in the representation theory of affine, quantum affine, and
extended affine Lie algebras and Lie superalgebras. They also highlighted
applications to conformal field theory, integrable and disordered systems.

Some of the articles are expository and accessible to a broad readership of
mathematicians and physicists interested in this area; others are research
articles that are appropriate for more advanced readers.

#### Readership

Graduate students and research mathematicians interested in infinite-dimensional Lie algebras and its applications in mathematical physics.

# Table of Contents

## Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory

- Table of Contents iii4 free
- Talks Presented v6 free
- Preface vii8 free
- Vertex Operator Algebras and the Representation Theory of Toroidal Algebras 110 free
- Symmetric Functions and Representations of Quantum Affine Algebras 2736
- Two Realizations of Toroidal sl2(C) 4756
- Vertex Lie Algebras, Vertex Poisson Algebras and Vertex Algebras 6978
- Type A Fusion Rules from Elementary Group Theory 97106
- Lie Algebra Automorphisms in Conformal Field Theory 117126
- On Lepowsky-Wilson's Z-Algebra 143152
- Scattering Rules in Soliton Cellular Automata Associated with Crystal Bases 151160
- Algebra Versus Analysis in Statistical Mechanics and Quantum Field Theory 183192
- Weak Modules and Logarithmic Intertwining Operators for Vertex Operator Algebras 201210
- Conjugate Bailey Pairs 227236
- Irreducibility of Affine Heeke Algebra Modules Induced from Specht Modules 257266
- Algebraic Structures behind Hilbert Schemes and Wreath Products 271280
- Some Generalizations of Genus Zero Two-Dimensional Conformal Field Theory 297306