Stability of the Non-Symmetric Space $E_7\mathrm{/}\mathrm{P}\mathrm{S}\mathrm{O}(8)$

We prove that the normal metric on the homogeneous space $E_7\mathrm{/}\mathrm{P}\mathrm{S}\mathrm{O}(8)$ is stable with respect to the Einstein-Hilbert action, thereby exhibiting the first known example of a non-symmetric metric of positive scalar curvature with this property.