3 problems

For a group $G$, let $G^{\vee}$ be its Langlands dual. Let $G_{\textrm{aff}}$ and $G^{\vee}_{\textrm{aff}}$ be the corresponding affine Kac–Moody groups, let $\lambda$ be a dominan…

Let $G$ be a reductive group, let $\Gamma_k$ be the group of roots of unity of order $k$ acting on $\mathbb A^2$ by $\zeta(x,y)=(\zeta x,\zeta^{-1}y)$, and consider the varieties c…

Let $G$ be an untwisted simply connected reductive group, let $G_{\aff}$ be its affine Kac–Moody group, and let the varieties constructed in the paper be transversal slices to…