On a generalization of a result of Howe for unipotent groups.

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 π. The aim of this paper is the determination of the space formed by the χ -semi-invariant vectors of π. [ABSTRACT FROM AUTHOR]