Contemporary Mathematics 1999; 469 pp; softcover Volume: 248 ISBN10: 0821811991 ISBN13: 9780821811993 List Price: US$110 Member Price: US$88 Order Code: CONM/248
 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. Readership 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 KacMoody 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 Walgebra of \({\mathfrak sl}(2,1)\): a construction from the quantization of screening operators
 L. Dolan  Affine algebras and nonperturbative 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 KnizhnikZamolodchikov equation with \(q=1\)
 E. Mukhin and A. Varchenko  Functorial properties of the hypergeometric map
 T. Nakashima  Polyhedral realizations of crystal bases and braidtype isomorphisms
 Y. Soibelman  Meromorphic tensor categories, quantum affine and chiral algebras I
 W. Wang  Dual pairs and infinite dimensional Lie algebras
