Contemporary Mathematics 2007; 474 pp; softcover Volume: 442 ISBN10: 0821839861 ISBN13: 9780821839867 List Price: US$133 Member Price: US$106.40 Order Code: CONM/442
 The articles in this book are based on talks given at the international conference "Lie algebras, vertex operator algebras and their applications", in honor of James Lepowsky and Robert Wilson on their sixtieth birthdays, held in May of 2005 at North Carolina State University. Some of the papers in this volume give inspiring expositions on the development and status of their respective research areas. Others outline and explore the challenges as well as the future directions of research for the twentyfirst century. The focus of the papers in this volume is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory. This book is useful for graduate students and researchers in mathematics and mathematical physics who want to be introduced to different areas of current research or explore the frontiers of research in the areas mentioned above. Readership Graduate students and research mathematicians interested in lie algebras, their representations, and generalizations. Table of Contents Lie algebras and related topics  K. Baur and N. Wallach  A class of gradings of simple Lie algebras
 S. Berman and J. Morita  Conjugacy results for the Lie algebra \(\mathfrak{sl}_2\) over an algebra which is a UFD
 V. Chari and A. Moura  KirillovReshetikhin modules associated to \(G_2\)
 R. Farnsteiner  Support spaces and AuslanderReiten components
 J. Feldvoss  On the cohomology of modular Lie algebras
 H. Garland  Eisenstein series on loop groups: MaassSelberg relations 4
 A. Hoshino  Generalized LittlewoodRichardson rule for exceptional Lie algebras \(E_6\) and \(F_4\)
 D. Nacin  An introduction to \(Q_n\) and its graph related quotients
 T. Nakashima  Affine geometric crystal of type \(G^{(1)}_2\)
 F. F. Nichita and D. Parashar  New constructions of YangBaxter systems
 V. Retakh, S. Serconek, and R. L. Wilson  Construction of some algebras associated to directed graphs and related to factorizations of noncommutative polynomials
 A. Savage  Geometric and combinatorial realizations of crystals of enveloping algebras
 H. Strade  Lie algebras of small dimension
Vertex (operator) algebras and related topics  I. I. Anguelova  Symmetric polynomials and \(H_D\)quantum vertex algebras
 M. J. Bergvelt  \(H_T\)vertex algebras
 C. Calinescu  On intertwining operators and recursions
 C. Dong and C. Jiang  Representations of vertex operator algebras
 J. Fuchs  On nonsemisimple fusion rules and tensor categories
 K. Hubbard  The duality between vertex operator algebras and coalgebras, modules and comodules
 J. Lepowsky  Some developments in vertex operator algebra theory, old and new
 H. Li  Twisted modules and quasimodules for vertex operator algebras
 G. Mason and M. P. Tuite  Chiral algebras and partition functions
 A. Milas  Modular forms and almost linear dependence of graded dimensions
 M. Primc  \((k,r)\)Admissible configurations and intertwining operators
 Z. Qin and W. Wang  Hilbert schemes of points on the minimal resolution and soliton equations
 C. Schweigert, J. Fuchs, and I. Runkel  Twining characters and Picard groups in rational conformal field theory
