The Quaternionic Cauchy-Szeg\"{o} Kernel on the Quaternionic Siegel Half Space

The quaternionic Cauchy-Szeg"{o} kernel of the Hardy space ${\mathcal{H}}^2({\mathcal{U}}_n)$ on the quaternionic Siegel half space ${\mathcal{U}}_n$ is derived and the Hardy spaces on the octonionic Siegel half space is investigated.