Fix $\mathbb{C}$ as the base field, and reductive groups are assumed to be connected.
Consider the example $SO_N\subset SL_N$. $SO_N$ is its own normalizer in $SL_N$, and the rank is much smaller, namely $[\dfrac{N-1}{2}]$, than the rank of $SL_N$. How can this be reflected in the Dynkin diagram of $SL_N$?
In Reductive subgroup corresponding to a subdiagram of the Dynkin diagram of a simple group one sees that Levi subgroups $L$ of a given semi-siimple group $G$ can be recovered from Dynkin subdiagrams of the diagram of $G$, and subgroups of maximal rank can be recovered similarly from extended Dynkin diagrams. Does the notion of maximal rank here means that the subgroups in question have the same rank as $G$ does?
If one works over a field $k$ not algebraically closed, is there a relative version of extended Dynkin diagram available for this kind of inclusion of subgroups, especially for those subgroup $H$ such that the normalizer $N(H,G)$ are of lower rank than $G$ itself?
Sorry for any misunderstanding about the cited mathoverflow discussions above, and references on extended Dynkin diagrams are also welcome.