The De Concini–Procesi compactification conjecture for Bethe subalgebras of Yangians

Let ${\mathfrak{g}}$ be a semisimple Lie algebra, let $Y({\mathfrak{g}})$ be its Yangian, and let $M_{\mathfrak{g}}$ be the De Concini–Procesi compactification of the regular part $T^{reg}$ of a Cartan torus, obtained by blowing up all indecomposable intersections of the hypersurfaces in the toric variety associated with the root hyperplanes. Parameter-space conjecture. $M_{\mathfrak{g}}$ is the parameter space for limit subalgebras of the family of Bethe subalgebras in the Yangian $Y({\mathfrak{g}})$. This generalizes the paper's result for ${\mathfrak{g}}={\mathfrak{gl}}_n$, where the parameter space is $\overline{M_{0,n+2}}$, and proposes the corresponding compactification for Yangians of other types.