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Limits of multiplicities in excellent filtrations and tensor product decompositions for affine Kac-Moody algebras. (English) Zbl 1426.17007
Summary: 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.
MSC:
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
05E10 Combinatorial aspects of representation theory
05A17 Combinatorial aspects of partitions of integers
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