4 problems

Path-reversal conjecture. In these Littelmann path models, $\widetilde{\Theta}$ is given by reversing Lakshmibai–Seshadri paths and translating the initial points of the reversed p…

Naito–Sagaki's conjecture. The irreducible summands of the restricted module should be indexed by those Littelmann paths whose restrictions become dominant.

Let $\mathbb{B}$ range over Littelmann path models for the irreducible representation $\operatorname{L}(\lambda)$, and let the branching property mean that the theorem asserting th…

Let $\mathfrak{g}=\mathfrak{sl}(2n,\mathbb{C})$, let $\mathfrak{g}^{\sigma}=\mathfrak{sp}(2n,\mathbb{C})$ be the fixed-point subalgebra, and let $\mathbb{B}$ be the path model for…