A note on the representation theory of central extensions of reductive $p$-adic groups

TL;DR

This paper demonstrates that key representation theory results for reductive p-adic groups also hold for their finite central extensions, broadening the understanding of these groups' representation structures.

Contribution

It extends fundamental representation theory results from reductive p-adic groups to their finite central extensions, filling a theoretical gap.

Findings

Key results extend to central extensions

Supports broader applicability of representation theory

Provides a foundation for future research

Abstract

In this note, we verify that several fundamental results from the theory of representations of reductive $p$-adic groups, extend to finite central extensions of these groups.