Let τ be the tensor product of
an anisotropic principal series representation of a free group Γ, not an endpoint
representation, with an irreducible unitary finite dimensional Γ-representation.
Usually τ is irreducible and has exactly two perfect boundary realizations. In a
certain well specified anomalous case τ splits into two irreducible components
and each component has exactly one boundary realization, which is not
perfect.