Two simple observations on representations of metaplectic groups

TL;DR

This paper provides a straightforward criterion for the irreducibility of non-unitary principal series representations of metaplectic groups, building on prior work that established irreducibility for the unitary case.

Contribution

It introduces a simple criterion for irreducibility of non-unitary principal series representations of metaplectic groups, extending previous results.

Findings

Established irreducibility criterion for non-unitary principal series

Connected results to prior irreducibility proofs for unitary cases

Simplified understanding of metaplectic group representations

Abstract

M. Hanzer and I. Matic have proved that the genuine unitary principal series representations of the metaplectic groups are irreducible. A simple consequence of that paper is a criterion for the irreducibility of the non-unitary principal series representations of the metaplectic groups that we give in this paper.