Symplectic Branching through Crystals

We give an alternative proof of Naito–Sagaki’s conjecture, which states that the restriction of $g{l}_{2n}(\mathbb{C})$-representations to $s{p}_{2n}(\mathbb{C})$ can be described in terms of crystals. Using the tableau model for crystals, we construct an explicit and self-contained bijection between their highest weight elements and Sundaram’s branching model.