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

by Berman, Stephen; Fendley, Paul; Huang, Yi-Zhi; Misra, Kailash; Parshall, Brian

• ISBN13: 9780821827161
• ISBN10: 0821827162
• Format: Paperback
• Copyright: 2002-07-01
• Publisher: Amer Mathematical Society

Summary

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. Thisconference 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 highlightedapplications 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.

Table of Contents

Talks Presented	v
Preface	vii
Vertex Operator Algebras and the Representation Theory of Toroidal Algebras	1	(26)
S. Berman
Y. Billig
J. Szmigielski
Symmetric Functions and Representations of Quantum Affine Algebras	27	(20)
V. Chari
M. Kleber
Two Realizations of Toroidal sl2 (c)	47	(22)
Ben Cox
Vertex Lie Algebras, Vertex Poisson Algebras and Vertex Algebras	69	(28)
C. Dong
H. Li
G. Mason
Type A Fusion Rules from Elementary Group Theory	97	(20)
A. Feingold
M. Weiner
Lie Algebra Automorphisms in Conformal Field Theory	117	(26)
J. Fuchs
C. Schweigert
On Lepowsky-Wilson's Z-Algebra	143	(8)
Y. Hara
M. Jimbo
H. Konno
S. Odake
J. Shiraishi
Scattering Rules in Soliton Cellular Automata Associated with Crystal Bases	151	(32)
G. Hatayama
A. Kuniba
M. Okado
T. Takagi
Y. Yamada
Algebra Versus Analysis in Statistical Mechanics and Quantum Field Theory	183	(18)
B. McCoy
Weak Modules and Logarithmic Intertwining Operators for Vertex Operator Algebras	201	(26)
A. Milas
Conjugate Bailey Pairs	227	(30)
A. Schilling
S. O. Warnaar
Irreducibility of Affine Hecke Algebra Modules Induced from Specht Modules	257	(14)
M. Vazirani
Algebraic Structures behind Hilbert Schemes and Wreath Products	271	(26)
W. Wang
Some Generalizations of Genus Zero Two-Dimensional Conformal Field Theory	297
W. Zhao