3 problems

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…

Let $G$ be a real connected reductive linear Lie group and $H$ a closed connected reductive subgroup of $G$. A compact quotient of $G/H$ is standard if it has the form…