On sufficient density conditions for lattice orbits of relative discrete series.

This note provides new criteria on a unimodular group G and a discrete series representation ( π , H π ) of formal degree d π > 0 under which any lattice Γ ≤ G with vol ( G / Γ ) d π ≤ 1 (resp. vol ( G / Γ ) d π ≥ 1 ) admits g ∈ H π such that π ( Γ ) g is a frame (resp. Riesz sequence). The results apply to all projective discrete series of exponential Lie groups.