On some results of Harish-Chandra for representations of p-adic groups, extended to their central extensions

The aim of this article is to give a complete proof of results of Harish-Chandra linking the irreducibility of parabolic induction of a supercuspidal representation of a p-adic group to the analytic behavior of the mu-function of Harish-Chandra and to show that the proof remains valid in the case of a central extension.M