Contemporary Mathematics 1985; 84 pp; softcover Volume: 46 ISBN10: 0821850482 ISBN13: 9780821850480 List Price: US$25 Member Price: US$20 Order Code: CONM/46
 The affine KacMoody algebra \(A_1^{(1)}\) has recently served as a source of new ideas in the representation theory of infinitedimensional affine Lie algebras. In particular, several years ago it was discovered that \(A_1^{(1)}\) and then a general class of affine Lie algebras could be constructed using operators related to the vertex operators of the physicists' string model. This book develops the calculus of vertex operators to solve the problem of constructing all the standard \(A_1^{(1)}\)modules in the homogeneous realization. Aimed primarily at researchers in and students of Lie theory, the book's detailed and concrete exposition makes it accessible and illuminating even to relative newcomers to the field. Table of Contents  The Lie algebra \(A_1^(1)\)
 The category \(\cal P_k\)
 The generalized commutation relations
 Relations for standard modules
 Basis of \(\Omega_L\) for a standard module \(L\)
 Schur functions
 Proof of linear independence
 Combinatorial formulas
