Restriction Problem for Anisotropic Principal Series of Free Groups

LetΓ0be a nonabelian free group and letπbe an anisotropic principal series representation ofΓ0. Exclude endpoint representations. Consider the restriction ofπto any cofinite subgroup. Usually the restriction is irreducible and has exactly two perfect boundary realizations. In a certain anomalous case the representation divides into two irreducible components, and each component has exactly one boundary realization, which is not perfect.