eBook ISBN:  9780821878385 
Product Code:  CONM/248.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821878385 
Product Code:  CONM/248.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 248; 1999; 469 ppMSC: Primary 17; Secondary 05
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.
ReadershipGraduate students and research mathematicians interested in mathematical physics and Lie theory; physicists.

Table of Contents

Articles

Georgia Benkart, SeokJin Kang, Hyeonmi Lee and DongUy Shin — The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine KacMoody algebras [ MR 1745252 ]

Stephen Berman and Shaobin Tan — A note on embeddings of some Lie algebras defined by matrices [ MR 1745253 ]

Stephen Berman and Jacek Szmigielski — Principal realization for the extended affine Lie algebra of type ${\rm sl}_2$ with coordinates in a simple quantum torus with two generators [ MR 1745254 ]

Vyjayanthi Chari and Nanhua Xi — Monomial bases of quantized enveloping algebras [ MR 1745255 ]

Jintai Ding and Boris Feigin — Quantized $W$algebra of $\mathfrak {sl}(2,1)$: a construction from the quantization of screening operators [ MR 1745256 ]

L. Dolan — Affine algebras and nonperturbative symmetries in superstring theory [ MR 1745257 ]

Chongying Dong and Kiyokazu Nagatomo — Automorphism groups and twisted modules for lattice vertex operator algebras [ MR 1745258 ]

P. Di Francesco — Truncated meanders [ MR 1745259 ]

Edward Frenkel and Nicolai Reshetikhin — The $q$characters of representations of quantum affine algebras and deformations of $\scr W$algebras [ MR 1745260 ]

Omar Foda and Trevor A. Welsh — Melzer’s identities revisited [ MR 1745261 ]

Robert L. Griess, Jr. — Automorphisms of lattice type vertex operator algebras and variations, a survey [ MR 1745262 ]

G. Hatayama, A. Kuniba, M. Okado, T. Takagi and Y. Yamada — Remarks on fermionic formula [ MR 1745263 ]

Naihuan Jing and Kailash C. Misra — $q$vertex operators for quantum affine algebras [ MR 1745264 ]

Shrawan Kumar — Homology of certain truncated Lie algebras [ MR 1745265 ]

J. Lepowsky — Vertex operator algebras and the zeta function [ MR 1745266 ]

Haisheng Li and Shuqin Wang — On ${\bf Z}$graded associative algebras and their ${\bf N}$graded modules [ MR 1745267 ]

Duncan J. Melville — An $A$form technique of quantum deformations [ MR 1745268 ]

Tetsuji Miwa and Yoshihiro Takeyama — Determinant formula for the solutions of the quantum KnizhnikZamolodchikov equation with $\vert q\vert =1$ [ MR 1745269 ]

E. Mukhin and A. Varchenko — Functorial properties of the hypergeometric map [ MR 1745270 ]

Toshiki Nakashima — Polyhedral realizations of crystal bases and braidtype isomorphisms [ MR 1745271 ]

Yan Soibelman — Meromorphic tensor categories, quantum affine and chiral algebras. I [ MR 1745272 ]

Weiqiang Wang — Dual pairs and infinite dimensional Lie algebras [ MR 1745273 ]


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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.

Articles

Georgia Benkart, SeokJin Kang, Hyeonmi Lee and DongUy Shin — The polynomial behavior of weight multiplicities for classical simple Lie algebras and classical affine KacMoody algebras [ MR 1745252 ]

Stephen Berman and Shaobin Tan — A note on embeddings of some Lie algebras defined by matrices [ MR 1745253 ]

Stephen Berman and Jacek Szmigielski — Principal realization for the extended affine Lie algebra of type ${\rm sl}_2$ with coordinates in a simple quantum torus with two generators [ MR 1745254 ]

Vyjayanthi Chari and Nanhua Xi — Monomial bases of quantized enveloping algebras [ MR 1745255 ]

Jintai Ding and Boris Feigin — Quantized $W$algebra of $\mathfrak {sl}(2,1)$: a construction from the quantization of screening operators [ MR 1745256 ]

L. Dolan — Affine algebras and nonperturbative symmetries in superstring theory [ MR 1745257 ]

Chongying Dong and Kiyokazu Nagatomo — Automorphism groups and twisted modules for lattice vertex operator algebras [ MR 1745258 ]

P. Di Francesco — Truncated meanders [ MR 1745259 ]

Edward Frenkel and Nicolai Reshetikhin — The $q$characters of representations of quantum affine algebras and deformations of $\scr W$algebras [ MR 1745260 ]

Omar Foda and Trevor A. Welsh — Melzer’s identities revisited [ MR 1745261 ]

Robert L. Griess, Jr. — Automorphisms of lattice type vertex operator algebras and variations, a survey [ MR 1745262 ]

G. Hatayama, A. Kuniba, M. Okado, T. Takagi and Y. Yamada — Remarks on fermionic formula [ MR 1745263 ]

Naihuan Jing and Kailash C. Misra — $q$vertex operators for quantum affine algebras [ MR 1745264 ]

Shrawan Kumar — Homology of certain truncated Lie algebras [ MR 1745265 ]

J. Lepowsky — Vertex operator algebras and the zeta function [ MR 1745266 ]

Haisheng Li and Shuqin Wang — On ${\bf Z}$graded associative algebras and their ${\bf N}$graded modules [ MR 1745267 ]

Duncan J. Melville — An $A$form technique of quantum deformations [ MR 1745268 ]

Tetsuji Miwa and Yoshihiro Takeyama — Determinant formula for the solutions of the quantum KnizhnikZamolodchikov equation with $\vert q\vert =1$ [ MR 1745269 ]

E. Mukhin and A. Varchenko — Functorial properties of the hypergeometric map [ MR 1745270 ]

Toshiki Nakashima — Polyhedral realizations of crystal bases and braidtype isomorphisms [ MR 1745271 ]

Yan Soibelman — Meromorphic tensor categories, quantum affine and chiral algebras. I [ MR 1745272 ]

Weiqiang Wang — Dual pairs and infinite dimensional Lie algebras [ MR 1745273 ]