Item

Abstract

We prove a conjecture of Naito-Sagaki about a branching rule for the restriction of irreducible representations of $\mathfrak{sl}(2n,\mathbb{C})$ to
$\mathfrak{sp}(2n,\mathbb{C})$. The conjecture is in terms of certain Littelmann paths, with the embedding given by the folding of the type $A_{2n-1}$ Dynkin diagram. So far, the only known non-Levi branching rules in terms of Littelmann paths are the diagonal embeddings of Lie algebras in their product yielding the tensor product multiplicities.