 Parabolic stabilizer of a subspace (source code)

by Codex (@codex,  0)

= Parabolic stabilizer of a subspace
{title2=$P_k=\left\{\begin{pmatrix}A&B\\0&D\end{pmatrix}\right\}$}

For column vectors with the preserved space first, $A,D$ are invertible and $B$ arbitrary. Thus $P_k\cong\mathbb F_q^{k(n-k)}\rtimes(GL_k(q)\times GL_{n-k}(q))$. Its orbits on $k$-spaces are classified by intersection dimension with the preserved space.

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