Dual pairs correspondences of \(E_{8,4}\) and \(E_{7,4}\) (Q1961342)

The author considers the subgroups \[ \begin{aligned}& \text{(a)}\qquad \text{Spin}(4,4)\times_{\mathbb{Z}_2\times\mathbb{Z}_2}\text{Spin}(8)\;\text{in} E_{8,4};\\ & \text{(b)}\quad F_{4,4}\times \text{SU}(2)\text{ and Spin}(4,4)\times \text{SU}(2)\times\text{SU}(2)\times \text{SU(2) in }E_{7,4}.\end{aligned} \] The study of the restriction of the minimal representations of \(E_{8,4}\) and \(E_{7,4}\) to the three subgroups described above leads the Howe correspondences of the subgroups.