7 problems

Let $G$ be a reductive group, let $B$ be a Borel subgroup, and let $Z^\mu$ be the finite-dimensional Zastava space associated with an element $\mu$ of the coroot lattice of $G$. Co…

Let $\mathfrak g_{\operatorname{aff},\varsigma}$ be the affine Lie algebra associated with $\mathfrak g',\sigma$, and $\zeta$, and let…

Generalized-minor cluster structure conjecture. Certain generalized minors give rise to a cluster structure on the trigonometric zastava.

Affine zastava conjecture. Theorem 1 and Theorem 2 should hold when $\mathfrak g$ is an untwisted affine algebra.

Completed localization conjecture. This equivalence extends to

Grading conjecture. The action of $bT^{(1)}$ on $fZ(CY_{ul{d}})$ extends to an action of $bT^{(1)}$, equivalently a grading, on both $widehat M$ and $\widehat{CY}_{ul{d}}$.

Splitting-module conjecture. This action extends to an action of $\widehat{CY}_{ul{d}}$, the completion of $CY_{ul{d}}$ at the maximal ideal of $fZ(CY_{ul{d}})^0$.