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

Abstract

AbstractWe 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.