Duality for spherical representations in exceptional theta correspondences

Loke, Hung; Savin, Gordan

doi:10.1090/tran/7471

Duality for spherical representations in exceptional theta correspondences
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by Hung Yean Loke and Gordan Savin PDF

Trans. Amer. Math. Soc. 371 (2019), 6359-6375 Request permission

Abstract:

We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type $\mathbf E_n$, to a split dual pair where one member is the exceptional group of the type $\mathbf {G}_2$. We prove that the correspondence gives a bijection between spherical representations if $n=6,7$, and a slightly weaker statement if $n=8$.

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