Summary: VERTEX OPERATOR ALGEBRAS AND IRREDUCIBILITY
OF CERTAIN MODULES FOR AFFINE LIE ALGEBRAS
DraŸ zen Adamovi' c
Department of Mathematics, University of Zagreb, Zagreb, Croatia
Abstract. We find the connection between the representation theory of vertex operator
algebra L(k\Lambda 0 ) and the irreducibility of tensor products V
(¯)\Omega L(k\Lambda 0 ). In the case of
affine Lie algebra A (1)
, on every admissible rational level we construct a family of irreducible
modules having infinitedimensional weight spaces.
Let g be a simple finitedimensional Lie algebra and “ g the associated affine Lie algebra.
Let V (¯) be a loop module for “ g corresponding to irreducible finitedimensional g--module
V (¯) and let L(–) be an irreducible highest weight “ g--module. Then the tensor product
(¯)\Omega L(–) has infinitedimensional weight spaces.
V. Chari and A. Pressley in [CP] studied these modules in the case when L(–) is the in
tegrable highest weight module. They proved that the “ g--module V
(¯)\Omega L(–) is irreducible