**Contemporary Mathematics**

Volume: 248;
1999;
469 pp;
Softcover

MSC: Primary 17;
Secondary 05

Print ISBN: 978-0-8218-1199-3

Product Code: CONM/248

List Price: $110.00

Individual Member Price: $88.00

**Electronic ISBN: 978-0-8218-7838-5
Product Code: CONM/248.E**

List Price: $110.00

Individual Member Price: $88.00

# Recent Developments in Quantum Affine Algebras and Related Topics

Share this page *Edited by *
*Naihuan Jing; Kailash C. Misra*

This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics.

Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying “center stage” in the theory of infinite dimensional Lie theory.

#### Table of Contents

# Table of Contents

## Recent Developments in Quantum Affine Algebras and Related Topics

- Contents vii8 free
- Preface ix10 free
- The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine Kac-Moody algebras 112 free
- A note on embeddings of some Lie algebras defined by matrices 3142
- Principal realization for the extended affine Lie algebra of type sl2 with coordinates in a simple quantum torus with two generators 3950
- Monomial bases of quantized enveloping algebras 6980
- Quantized W-algebra of sl(2, 1): A construction from the quantization of screening operators 8394
- Affine algebras and non-perturbative symmetries in superstring theory 109120
- Automorphism groups and twisted modules for lattice vertex operator algebras 117128
- Truncated meanders 135146
- The q-characters of representations of quantum affine algebras and deformations of W-algebras 163174
- Melzer's identities revisited 207218
- Automorphisms of lattice type vertex operator algebras and variations, a survey 235246
- Remarks on fermionic formula 243254
- q-vertex operators for quantum affine algebras 293304
- Homology of certain truncated Lie algebras 309320
- Vertex operator algebras and the zeta function 327338
- On Z-graded associative algebras and their N-graded modules 341352
- An A-form technique of quantum deformations 359370
- Determinant formula for the solutions of the quantum Knizhnik-Zamolodchikov equation with |q| = 1 377388
- Functorial properties of the hypergeometric map 395406
- Polyhedral realizations of crystal bases and braid-type isomorphisms 419430
- Meromorphic tensor categories, quantum affine and chiral algebras I 437448
- Dual pairs and infinite dimensional Lie algebras 453464

#### Readership

Graduate students and research mathematicians interested in mathematical physics and Lie theory; physicists.