It's all in the title: Are Wolf spaces flag manifolds? Both are group quotients of semi-simple Lie groups. In the Grassmannian case this is so, and I always tacitly assumed it extended to the general case. However, I recently read this post by Moroianu, where he says that
the quaternionic projective spaces $ℍP_n$ are quaternion-Kähler, but have no almost complex structure
I now think my assumption is probably false. Can someone please help "de-confuse" me?