The volumes of Miyauchi subgroups

TL;DR

This paper computes the volumes of Miyauchi subgroups associated with generic representations of the unramified unitary group of rank three, extending the understanding of local newforms and their structural properties.

Contribution

It provides explicit volume calculations for Miyauchi subgroups, a novel contribution to the study of local representations of unitary groups.

Findings

Volumes of Miyauchi subgroups are explicitly calculated.

Results relate to the structure of local newforms.

Enhances understanding of unramified unitary groups.

Abstract

Miyauchi described the $L$ and $\varepsilon$-factors attached to generic representations of the unramified unitary group of rank three in terms of local newforms defined by a sequence of subgroups. We calculate the volumes of these Miyauchi groups.