Depth Zero Representations of Nonlinear Covers of $p$-adic Groups

TL;DR

This paper extends Moy-Prasad methods to define and analyze depth zero genuine representations of nonlinear covers of p-adic groups, successfully constructing all depth zero supercuspidal representations of the metaplectic group over such fields.

Contribution

It introduces a generalized framework for depth zero representations of nonlinear p-adic group covers and explicitly constructs all such supercuspidal representations for the metaplectic group.

Findings

Constructed all depth zero supercuspidal representations of $Mp_{2n}$.

Generalized Moy-Prasad methods to nonlinear covers.

Provided a new approach to studying representations of nonlinear p-adic groups.

Abstract

We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over $p$-adic local fields. In particular, we construct all depth zero supercuspidal representations of the metaplectic group $Mp_{2n}$ over a $p$-adic field of odd residue characteristic.