On a generalization of a result of Howe for unipotent groups

Abstract

Let F be a nonarchimedean local field of characteristic zero and G be a unipotent algebraic group defined over F. The set of rational points of G, denoted by G, is a p-adic Lie group. Let $g$ be the Lie algebra of G. Now let H be a normal closed subgroup of G, χ be a unitary character of H and π be an irreducible unitary representation of G in a Hilbert space $H_{\pi }$. The aim of this paper is the determination of the space formed by the χ-semi-invariant vectors of π.