  We prove that irreducible complex representations of finitely generated
nilpotent groups are monomial if and only if they have finite weight, which was
conjectured by Parshin. Note that we consider (possibly, infinite-dimensional)
representations without any topological structure. Besides, we prove that for
certain induced representations, irreducibility is implied by Schur
irreducibility. Both results are obtained in a more general form for
representations over an arbitrary field.
