  We prove a special case of 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. We propose and motivate an
approach to the conjecture in general, in terms of Littlewood-Richardson
Sundaram tableaux.
