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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 $\mathbb Z/2\mathbbZ$ acts on $T$ by the inverse involution. We describe the correspondence ofrepresentations arising by restricting the minimal representation.

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