${\mathrm{SL}}_4(\mathbf{Z})$ is not purely matricial field

Michael Magee, Mikael de la Salle

We prove that every finite dimensional unitary representation of ${\mathrm{SL}}_4(\mathbf{Z})$ contains a non-zero ${\mathrm{SL}}_2(\mathbf{Z})$-invariant vector. As a consequence,…