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Recent Developments in Quantum Affine Algebras and Related Topics
Edited by: Naihuan Jing and Kailash C. Misra, North Carolina State University, Raleigh, NC

Contemporary Mathematics
1999; 469 pp; softcover
Volume: 248
ISBN-10: 0-8218-1199-1
ISBN-13: 978-0-8218-1199-3
List Price: US$110
Member Price: US$88
Order Code: CONM/248
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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.


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

Table of Contents

  • G. Benkart, S.-J. Kang, H. Lee, and D.-U. Shin -- The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine Kac-Moody algebras
  • S. Berman and S. Tan -- A note on embeddings of some Lie algebras defined by matrices
  • S. Berman and J. Szmigielski -- Principal realization for the extended affine Lie algebra of type \(sl_2\) with coordinates in a simple quantum torus with two generators
  • V. Chari and N. Xi -- Monomial bases of quantized enveloping algebras
  • J. Ding and B. Feigin -- Quantized W-algebra of \({\mathfrak sl}(2,1)\): a construction from the quantization of screening operators
  • L. Dolan -- Affine algebras and non-perturbative symmetries in superstring theory
  • C. Dong and K. Nagatomo -- Automorphism groups and twisted modules for lattice vertex operator algebras
  • P. Di Francesco -- Truncated meanders
  • E. Frenkel and N. Reshetikhin -- The \(q\)-characters of representations of quantum affine algebras and deformations of \(\mathcal W\)-algebras
  • O. Foda and T. A. Welsh -- Melzer's identities revisited
  • R. L. Griess, Jr. -- Automorphisms of lattice type vertex operator algebras and variations, a survey
  • G. Hatayama, A. Kuniba, M. Okado, T. Takagi, and Y. Yamada -- Remarks on fermionic formula
  • N. Jing and K. C. Misra -- \(q\)-vertex operators for quantum affine algebras
  • S. Kumar -- Homology of certain truncated Lie algebras
  • J. Lepowsky -- Vertex operator algebras and the zeta function
  • H. Li and S. Wang -- On \(\mathbb Z\)-graded associative algebras and their \(\mathbb N\)-graded modules
  • D. J. Melville -- An \(\mathbb A\)-form technique of quantum deformations
  • T. Miwa and Y. Takeyama -- Determinant formula for the solutions of the quantum Knizhnik-Zamolodchikov equation with \(|q|=1\)
  • E. Mukhin and A. Varchenko -- Functorial properties of the hypergeometric map
  • T. Nakashima -- Polyhedral realizations of crystal bases and braid-type isomorphisms
  • Y. Soibelman -- Meromorphic tensor categories, quantum affine and chiral algebras I
  • W. Wang -- Dual pairs and infinite dimensional Lie algebras
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