On a conjecture of Naito-Sagaki: Littelmann paths and Littlewood-Richardson Sundaram tableaux

In recent work with Schumann we have proven a conjecture of Naito-Sagaki giving branching rule for the decomposition restriction an irreducible representation special linear Lie algebra to symplectic algebra, therein embedded as fixed-point set involution obtained by folding corresponding Dyinkin diagram. It provides new approach rules non-Levi subalgebras in terms Littelmann paths. this paper motivate result, provide examples, and give overview combinatorics involved its proof.