Generic irreducibility of parabolic induction for real reductive groups

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.