RESTRICTING COHOMOLOGICAL REPRESENTATIONS OF SO0(n,1) AND SU(n,1)

Let G denote either SO 0(n,1) or SU (n,1). We study restrictions of cohomological representations of G to subgroups H isomorphic to SO 0(m,1) or SU (m,1). We prove that such a restriction contains, as a subrepresentation, some cohomological representation of H. When G = SU(n,1), we extend a result of Delorme by showing that cohomological representations are non-spherical in a strong sense: if H is isomorphic to SU (m,1) (with 1 ≤ m ≤ n), then the restriction of a cohomological representation to H is non-spherical.

Nilpotent Orbits and Whittaker Functions for Derived Functor Modules of Sp(2, ℝ)

We study the moderate growth generalized Whittaker functions, associated to a unitary character ψ of a unipotent subgroup, for the non-tempered cohomological representation of G = Sp(2, ℝ). Through an explicit calculation of a holonomic system which characterizes these functions we observe that their existence is determined by the including relation between the real nilpotent coadjoint G-orbit of ψ in and the asymptotic support of the cohomological representation.