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  "body": "\n## Summary\n\nA flag manifold is a quotient $G/P$ of a connected complex semisimple Lie group $G$ by a parabolic subgroup $P$.\nThe basic example is the space of complete flags $V_1 \\subset V_2 \\subset \\cdots \\subset V_{n-1}$ of subspaces of $\\C^n$ with $\\dim V_i = i$.\nProjective spaces and Grassmannians are flag manifolds too.\nFlag manifolds are compact complex manifolds on which $G$ acts, and they carry the geometry behind the Borel–Weil theorem and Schubert calculus.\n\n## Explanations\n\n### L1 human\n\nA flag in $\\C^3$ is a line through the origin together with a plane that contains it, like a flagpole and a flag.\nThe set of all such flags is a smooth, compact space of complex dimension $3$.\nInvertible matrices move flags around, and any flag can be moved to any other.\nSo the space of flags is a group divided by the subgroup that fixes one flag, the upper triangular matrices.\nOther flag manifolds keep only some of the subspaces, as the projective plane keeps only the line.\n",
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