The orthogonal Grassmannian $OG(k,n)$ is the set of all isotropic $k$ dimensional subspaces of a $n$ dimensional subspaces with respect to a non-degenerate symmetric bilinear form. Is it isomorphic to a $SO(n)/P_k$ where $P_k$ is the maximal parabolic subgroup with respect to a simple root ?
2026-03-25 12:13:46.1774440826
Orthogonal Grassmannian
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