Notes on unitary theta representations of compact groups

TL;DR

This paper explores the properties of unitary theta representations of compact groups within the context of Howe correspondences, focusing on induction and restriction functors.

Contribution

It advances understanding of theta representations of compact groups by establishing new results on their behavior under induction and restriction.

Findings

Proved new results on unitary theta representations of compact groups.

Analyzed the behavior of these representations with respect to induction and restriction.

Contributed to the broader understanding of Howe correspondences in this setting.

Abstract

We continue our work on understanding Howe correspondences by using theta representations from p-adic groups to compact groups. We prove some results for unitary theta representations of compact groups with respect to the induction and restriction functors.