An approach to the branching rule from to via Littelmannʹs path model

We propose a conjecture describing the branching rule, in terms of Littelmannʹs path model, from the special linear Lie algebra (of type A2n−1) to the symplectic Lie algebra (of type Cn) embedded as the fixed point subalgebra of the diagram automorphism of . Moreover, we prove the conjecture in certain cases, and also provide some supporting examples. In addition, we show that the branching coefficients can be obtained explicitly by using the inverse Kostka matrix and path models for tensor products of symmetric powers of the defining (or natural) representation of .