Whittaker models for depth zero representations of covering groups

TL;DR

This paper investigates the dimensions of Whittaker models for depth zero representations of covering groups, specifically for Brylinski-Deligne coverings of GL(n), extending prior theoretical work.

Contribution

It provides explicit dimension formulas for Whittaker models in the context of Brylinski-Deligne coverings of GL(n), advancing understanding of representation theory for covering groups.

Findings

Dimensions of Whittaker models are determined for Brylinski-Deligne coverings of GL(n)

Results align with previous work by Howard, Blondel, and others

The study enhances the theoretical framework for depth zero representations

Abstract

We study the dimension of the space of Whittaker functionals for depth zero representations of covering groups. In particular, we determine such dimensions for arbitrary Brylinski-Deligne coverings of the general linear group. The results in the paper are motivated by and compatible with the work of Howard and the second author, and earlier work by Blondel.