A family of Spin(8) dual pairs: the case of real groups

Wee Teck Gan, Hung Yean Loke, Annegret Paul, Gordan Savin

Published 2023-02-05Version 1

Exceptional groups of type $E_6$ contain dual pairs where one member is $\mathrm{Spin}(8)$, and the other is $T\rtimes \mathbb Z/2\mathbb Z$, where $T$ is a two-dimensional torus and the non-trivial element in $\mathbb Z/2\mathbb Z$ acts on $T$ by the inverse involution. We describe the correspondence of representations arising by restricting the minimal representation.