Tensor Product Decompositions for Affine Kac-Moody Algebras

The decomposition into irreducible modules is determined, for the tenser product of two arbitrary irreducible integrable highest weight modules, for an (untwisted) affine Kac-Moody algebra L. The result is applied 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 construction), V-ir the Virasoro algebra, is also briefly investigated