Correspondances de Howe pour les groupes des similitudes

TL;DR

This paper extends Howe correspondences to similitude groups over p-adic fields, building on Roberts' work on groups like GSp and GO, to deepen understanding of their representation theory.

Contribution

It introduces a new method to define Howe correspondences specifically for similitude groups over p-adic fields, expanding the scope of previous frameworks.

Findings

Established Howe correspondences for similitude groups over p-adic fields.

Connected the work to existing theories on GSp and GO groups.

Provided a foundation for further research in representation theory of similitude groups.

Abstract

In this paper, we give a way to define the Howe correspondences for the similitudes groups over p-adic fields by following the work of Brooks Roberts on the groups (GSp, GO).