5 problems

Let $G_0$ be a real reductive linear Lie group, and let $K_0$ be its maximal compact subgroup. Fix an Iwasawa decomposition … of $G_0$, where $A_0$ is abelian and normalizes $N_0$.…

Distinctness conjecture. Distinct points of $X_\Phi$ correspond to distinct limit commutative subalgebras in the Yangian $Y(\mathfrak g)$.

Multiplicity equality conjecture. Is it exactly equal, that is, does

Generalization conjecture. Do the results of Theorem hold for any semisimple adjoint group $G$?

Wonderful compactification conjecture. The normalized wonderful compactification of $\mathfrak{X}^0_\Gamma(G)$ should be a simply connected compactification of…