TENSOR PRODUCT DECOMPOSITIONS FOR AFFINE KAC-MOODY ALGEBRAS

The decomposition into irreducible modules is determined, for the tens er product of two arbitrary irreducible integrable highest weight modu les, for an (untwisted) affine Kac-Moody algebra L. The result is appl ied to investigate full multiplicity regions and cyclic modules within the tenser product space for an affine Kac-Moody algebra. The tenser product decomposition into irreducible modules over L+ V-ir (Coset con struction), V-ir the Virasoro algebra, is also briefly investigated.