We prove that there exists no irreducible representation of the identity component of the isometry group ${ \rm PO}(1,n)$ of the real hyperbolic space of dimension $n$ into the group ${ \rm O}(2,\infty)$, if $n\geq 3$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of ${ \rm PO}(1,n)^{ \circ}$ into the groups ${ \rm O}(p,\infty)$ for other values of $p$.
Categories: math.GR math.RT