**Contemporary Mathematics**

Volume: 442;
2007;
474 pp;
Softcover

MSC: Primary 17; 81; 82;

**Print ISBN: 978-0-8218-3986-7
Product Code: CONM/442**

List Price: $133.00

AMS Member Price: $106.40

MAA Member Price: $119.70

**Electronic ISBN: 978-0-8218-8121-7
Product Code: CONM/442.E**

List Price: $133.00

AMS Member Price: $106.40

MAA Member Price: $119.70

# Lie Algebras, Vertex Operator Algebras and Their Applications

Share this page *Edited by *
*Yi-Zhi Huang; Kailash C Misra*

The articles in this book are based on talks given at the
international conference “Lie algebras, vertex operator algebras
and their applications”, in honor of James Lepowsky and Robert
Wilson on their sixtieth birthdays, held in May of 2005 at North
Carolina State University. Some of the papers in this volume give
inspiring expositions on the development and status of their
respective research areas. Others outline and explore the challenges
as well as the future directions of research for the twenty-first
century. The focus of the papers in this volume is mainly on Lie
algebras, quantum groups, vertex operator algebras and their
applications to number theory, combinatorics and conformal field
theory.

This book is useful for graduate students and researchers in mathematics and
mathematical physics who want to be introduced to different areas of current
research or explore the frontiers of research in the areas mentioned above.

#### Readership

Graduate students and research mathematicians interested in lie algebras, their representations, and generalizations.

# Table of Contents

## Lie Algebras, Vertex Operator Algebras and Their Applications

- Contents v6 free
- Preface vii8 free
- Biographies of James Lepowsky and Robert Wilson xi12 free
- List of Ph.D. Students xiii14 free
- List of Talks xv16 free
- List of Participants xix20 free
- Lie algebras and related topics 124 free
- A Class of Gradings of Simple Lie Algebras 326
- Conjugacy Results for the Lie Algebra sI2 over an Algebra Which is a UFD 1740
- Kirillov-Reshetikhin Modules Associated to G2 4164
- Support Spaces and Auslander-Reiten Components 6184
- On the Cohomology of Modular Lie Algebras 89112
- Eisenstein Series on Loop Groups: Maass-Selberg Relations 4 115138
- Generalized Littlewood-Richardson Rule for Exceptional Lie Algebras E6 and F4 159182
- An Introduction to Qn and Its Graph Related Quotients 171194
- Affine Geometric Crystal of Type G2(1) 179202
- New Constructions of Yang-Baxter Systems 193216
- Construction of Some Algebras Associated to Directed Graphs and Related to Factorizations of Noncommutative Polynomials 201224
- Geometric and Combinatorial Realizations of Crystals of Enveloping Algebras 221244
- Lie algebras of Small Dimensiou 233256

- Vertex (operator) algebras and related topics 267290
- Symmetric Polynomials and HD-Quantum Vertex Algebras 269292
- HT-Vertex Algebras 279302
- On Intertwining Operators and Recursions 289312
- Representations of Vertex Operator Algebras 303326
- On Non-Semisimple Fusion Rules and Tensor Categories 315338
- The Duality between Vertex Operator Algebras and Coalgebras, Modules and Comodules 339362
- Some Developments in Vertex Operator Algebra Theory, Old and New 355378
- Twisted Modules and Quasi-Modules for Vertex Operator Algebras 389412
- Chiral Algebras and Partition Functions 401424
- Modular Forms and Almost Linear Dependence of Graded Dimensions 411434
- ( k, r )-Admissible Configurations and Intertwining Operators 425448
- Hilbert Schemes of Points on the Minimal Resolution and Soliton Equations 435458
- Twining Characters and Picard Groups in Rational Conformal Field Theory 463486