On sufficient density conditions for lattice orbits of relative discrete series

Abstract

This note provides new criteria on a unimodular group $G$ and a discrete series representation $(\pi ,{\mathcal{H}}_{\pi })$ of formal degree $d_{\pi }>0$ under which any lattice $\Gamma \le G$ with $\text{vol}(G/\Gamma )d_{\pi }\le 1$ (resp. $\text{vol}(G/\Gamma )d_{\pi }\ge 1$) admits $g\in {\mathcal{H}}_{\pi }$ such that $\pi (\Gamma )g$ is a frame (resp. Riesz sequence). The results apply to all projective discrete series of exponential Lie groups.

9 pages

References in corpus (1)

• The density theorem for projective representations via twisted group von Neumann algebras