The external semidirect product  of  an algebra of invariant differential operators and  an algebra of -invariant rational functions, where t is an induced unitary representation of a nilpotent Lie group G by a character c of a connected and simply connected subgroup H has been constructed. This construction is used to devise the abstract set  of annihilators of the so-called Frobenius vectors. It also allows to endow the space of covariant distribution vectors  with an -almost module structure.