Let $G$ be a compact simple Lie group. Choose a system of positive roots, and let $\mathrm{SU}(2) \subset G$ correspond to the highest root, and $\mathbb{Z}/2 \subset \mathrm{SU}(2)$ the centre. The centralizer of this $\mathbb{Z}/2$ inside of $G$ is a subgroup $H \subset G$ of shape $\mathrm{SU}(2) \circ K = (\mathrm{SU}(2) \times K) / (\mathbb{Z}/2)$. The Dynkin diagram for $H$ can be found by drawing the affine dynkin diagram for $G$, and deleting the node(s) adjacent to the affine root. The now-isolated affine root is the copy of $\mathrm{SU}(2)$, and the rest of the Dynkin diagram for $K$. In the type-A case, $H$ is reductive but not simple, picking up a $\mathrm{U}(1)$ factor; this is because in that case the affine root had two neighbours, not just one. The list of $H$'s is available in the Wikipedia article Quaternion-Kähler symmetric space, because the quotient spaces $G/H$ are precisely the *quaternionic symmetric spaces*.

Standard arguments then say that $G$ has a real form with maximal compact $H$. It is not the compact form (except for $G = H = \mathrm{SU}(2)$), and it is usually not the split real form. Rather, it is a third canonical real form for any group. For the classical series, it is $\mathrm{SU}(2,n-2)$, $\mathrm{SO}(4,n-4)$, and $\mathrm{Sp}(1,n-1)$. If I am reading Wikipedia correctly, then, together with $\mathrm{SO}(3,n-3)$, these are the real forms that admit quaternionic discrete series representations.

Does this canonical real form have a standard name in the literature?