Abstract
The decomposition into irreducible modules is determined, for the tensor 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 tensor product space for an affine Kac-Moody algebra. The tensor product decomposition into irreducible modules over L ⊕ Vir (Coset construction), Vir the Virasoro algebra, is also briefly investigated.
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