Semi-invariant distribution vectors for p-adic unipotent groups

Let G be a unipotent algebraic group defined over a p-adic field of characteristic zero. We denote by G the set of rational points of G. It is a p-adic Lie group with Lie algebra denoted by g. Let pi be an irreducible unitary representation of G in a Hilbert space H-pi, f be a linear form on g and h be a polarization at f. We denote by chi(f) a character of H = exp(h) related to f. The aim of this study is to give a precise description of the space of semi-invariant distribution vectors (H-pi(-infinity))(H,chi f) of pi.