Principal series representations of metaplectic groups

TL;DR

This paper investigates the principal series representations of metaplectic groups, computes their Plancherel measure via Eisenstein series, and constructs genuine central characters in the simply-laced case, advancing understanding of their harmonic analysis.

Contribution

It introduces explicit calculations of Plancherel measures and constructs genuine central characters for metaplectic groups, providing new tools for their harmonic analysis and representation theory.

Findings

Computed Plancherel measure using Eisenstein series

Constructed genuine central characters in the simply-laced case

Enhanced understanding of harmonic analysis on metaplectic groups

Abstract

We study the principal series representations of central extensions of a split reductive algebraic group by a cyclic group of order $n$. We compute the Plancherel measure of the representation using Eisenstein series and a comparison method. In addition, we construct genuine central characters of the metaplectic torus in the simply-laced case.