  We prove a generalization of Schur orthogonality relations for certain
classes of representations of Gromov hyperbolic groups. We apply the obtained
results to show that representations of non-abelian free groups associated to
the Patterson-Sullivan measures corresponding to a wide class of invariant
metrics on the group are monotonous in the sense introduced by Kuhn and Steger.
This in particular includes representations associated to harmonic measures of
a wide class of random walks.
