Non-vanishing unitary cohomology of low-rank integral special linear groups

Benjamin Brück, Sam Hughes, Dawid Kielak +1

We construct explicit finite-dimensional orthogonal representations $\ddot{I}{€}_N$ of ${\mathrm{SL}}_N(\mathbb{Z})$ for $N\in \{3,4\}$ all of whose invariant vectors are trivial, an…