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

TL;DR

This paper provides a complete proof of Harish-Chandra's results relating irreducibility of parabolic induction to the mu-function, extending these results to central extensions of p-adic groups.

Contribution

It offers a comprehensive proof of Harish-Chandra's results and demonstrates their validity in the context of central extensions of p-adic groups.

Findings

Proved the link between irreducibility and the mu-function for p-adic groups.

Extended Harish-Chandra's results to central extensions.

Confirmed the proof's validity in the extended setting.

Abstract

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