3 problems

Let $G/H$ be a homogeneous space in the reductive setting, let $\mathfrak g$ and $\mathfrak h$ be the Lie algebras of $G$ and $H$, and let $\mathfrak h^{\perp}\subset\mathfrak g^*$…

Standard quotient conjecture. The homogeneous space $G/H$ admits a cocompact properly discontinuous group if and only if $G/H$ admits a compact standard quotient.

Let $G/H$ be a reductive homogeneous space in Setting, and let $\operatorname{Disc}(G/H)$ denote its discrete series representations. Kobayashi's conjecture. One has the equivalenc…