Multiplicity free Weil representations arising from exceptional groups

TL;DR

This paper demonstrates that specific Weil representations associated with exceptional groups are multiplicity free and identifies their irreducible quotients using exceptional theta correspondences.

Contribution

It introduces a novel approach to analyze Weil representations of p-adic groups via exceptional theta correspondences, establishing multiplicity freeness and classifying quotients.

Findings

Proves multiplicity freeness of certain Weil representations.

Determines irreducible quotients of these representations.

Utilizes exceptional theta correspondences for analysis.

Abstract

Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.