5 problems

Extended Horn cone conjecture. If $(\lambda,\mu,\nu)\in\overline{{\operatorname{EH}}}(n)$, then

Strong eigencone functoriality along folds. Along the folds of $\phi$, one has

Let $G$ be a connected semisimple complex algebraic group, and let $M\subseteq G$ be the fixed subgroup of a diagram automorphism of $G$. The strong eigencone functoriality conject…

The PRV conjecture. If there exist $u,v,w\in W$ such that

Let $G$ be a connected simply-connected, semisimple complex algebraic group, let $\sigma$ be a diagram automorphism of $G$, and let $K$ be its fixed subgroup. Fix a standard parabo…