I'm reading Wilson's book "The Finite Simple Groups", specifically the sections on the orthogonal groups. (See: http://link.springer.com/book/10.1007%2F978-1-84800-988-2)
In section 3.7.4, he discusses subgroups of the orthogonal groups.
The Dynkin diagram for the plus-type orthogonal group of dimension $2m$ is $D_m$.
(To be clear, "plus-type" means the group preserving a form of maximal Witt index $m$.)
Furthermore, the nodes along the "stem" of $D_m$ correspond to isotropic spaces of dimension $1,2,\ldots,m-2$, while the remaining 2 nodes correspond to the 2 orbits of $m$-dimensional isotropic spaces under $SO_{2m}^+(q)$.
The correspondence has the property that if you delete a node from the Dynkin diagram, the remaining diagram corresponds to a group which is a Levi complement of the stabilizer of the appropriate isotropic subspace.
My question is:
Why are $m-1$ dimensional isotropic spaces left out of this? Are they somehow different from the others?