Geometric quantization conjecture for discrete series of reductive homogeneous spaces

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 $\mathfrak h^{\perp}\subset\mathfrak g^*$ be the annihilator of $\mathfrak h$. Let $\operatorname{Disc}(G/H)$ denote the discrete-series representations of $G/H$. Geometric quantization conjecture. Every $\pi\in\operatorname{Disc}(G/H)$ is obtained as a geometric quantization of an elliptic coadjoint orbit that meets $\mathfrak h^{\perp}$.

This conjecture proposes a geometric description of all discrete-series representations. The source presents it as the geometric part of an exhaustion problem after the existence of discrete series is established; no general resolution is supplied.