Exceptional dual pair correspondences; case of real groups of split rank one

TL;DR

This paper investigates the representation theory of exceptional real groups with split rank one, focusing on dual pairs involving quaternionic forms and the split Lie group of type G2, revealing new correspondence results.

Contribution

It establishes new results on the restriction of minimal representations of quaternionic groups to dual pairs involving split rank one groups, expanding understanding of their representation correspondences.

Findings

Significant results on the representation correspondence for dual pairs in quaternionic groups.

New insights into the restriction of minimal representations to dual pairs.

Advances in understanding the structure of exceptional real groups of split rank one.

Abstract

Exceptional real groups have quaternionic forms of split rank 4 that contain dual pairs $G\times G'$, where $G'$ is the split Lie group of the type $G_2$, and $G$ a Lie group of split rank one. In this paper we restrict the minimal representation of the quaternionic group to the dual pair and prove some significant results for the resulting correspondence of representations.