The nonexistence conjecture for cocompact quotients of $SL(n,\mathbb{R})/SL(m,\mathbb{R})$

Let $m<n$ and let $[?]$ be a non-trivial homomorphism from $SL(m,\mathbb{R})$ to $SL(n,\mathbb{R})$.

Nonexistence conjecture. The homogeneous space

$$SL(n,\mathbb{R})/\psi(SL(m,\mathbb{R}))$$

does not admit a cocompact discontinuous group.

This is stated as a special case of the standard quotient conjecture. The supplied text gives no resolution status.