Recent Developments in Quantum Affine Algebras and Related Topics: Representations of Affine and Quantum Affine Algebras and Their Applications, North Carolina State University, May 21-24, 1998(Contemporary Mathematics)

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