Limits of Multiplicities in Excellent Filtrations and Tensor Product   Decompositions for Affine Kac-Moody Algebras
  We express the multiplicities of the irreducible summands of certain tensor products of irreducible integrable modules for an affine Kac-Moody algebra over a simply laced Lie algebra as sums of multiplicities in appropriate excellent filtrations (Demazure flags). As an application, we obtain expressions for the outer multiplicities of tensor products of two fundamental modules for $\widehat{\mathfrak{sl}}_2$ in terms of partitions with bounded parts, which subsequently lead to certain partition identities. 
Dijana Jakeli\'c, Adriano Moura
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