# Duality for spherical representations in exceptional theta correspondences

## TL;DR

This paper investigates the exceptional theta correspondence for real groups derived from the minimal representation of split exceptional groups, establishing bijections between spherical representations for certain group types.

## Contribution

It proves the theta correspondence induces bijections between spherical representations for E_6 and E_7, and a weaker form for E_8, advancing understanding of exceptional dual pairs.

## Key findings

- Bijection between spherical representations for E_6 and E_7
- Weaker correspondence result for E_8
- Enhanced understanding of exceptional theta correspondences

## Abstract

We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type E_n, to a split dual pair where one member is the exceptional group of the type G_2. We prove that the correspondence gives a bijection between spherical representations if n=6,7, and a slightly weaker statement if n=8.