Similitude exceptional theta correspondences

TL;DR

This paper develops a similitude version of exceptional theta correspondences, extending key tools like the Howe duality theorem and seesaw identity from isometry to similitude groups, advancing the theoretical framework.

Contribution

It introduces a similitude framework for exceptional theta correspondences and generalizes foundational tools like Howe duality and seesaw identities to this setting.

Findings

Howe duality theorem holds in the similitude setting

Seesaw identity extends to similitude dual pairs

Framework unifies isometry and similitude cases

Abstract

We construct and develop a similitude version of exceptional theta correspondences and show that the Howe duality theorem follows from that for the "isometry" case. We also extend basic tools such as the seesaw identity associated to seesaw dual pairs to the similitude setting.