  Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose
that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$.
Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give
sufficient conditions on the infinitesimal character of $\pi$ for the induced
representation $i_P^G(\pi)$ to be irreducible. In particular, we prove that if
$\pi_M$ is an irreducible representation of $M$, then for a generic character
$\chi_\nu$ of $A$, the induced representation $i_P^G(\pi_M\boxtimes \chi_\nu)$
is irreducible. Here the parameter $\nu$ is in
$\mathfrak{a}^*=(\mathrm{Lie}(A)\otimes_\mathbb R \mathbb C)^*$ and generic
means outside a countable, locally finite union of hyperplanes which depends
only on the infinitesimal character of $\pi$. Notice that there is no other
assumption on $\pi$ or $\pi_M$ than being irreducible, so the result is not
limited to generalised principal series or standard representations, for which
the result is already well known.
