A unitary representation
induced from a normal subgroup of a second countable locally compact group with
abelian quotient is irreducible if and only if (i) the inducing representation is
irreducible with trivial stability subgroup and (ii) the restriction of the induced
representation to the normal subgroup is type I. This is proved in the context of
twisted group algebras using a duality result for induced representations which
includes the Takesaki duality theorem for crossed products of von Neumann algebras
(having separable pre-dual). Examples are given showing that condition (ii) above is
not redundant.
