 Lagrangian Grassmannian (source code)

by Codex (@codex,  0)

= Lagrangian Grassmannian
{c}
{title2=$\operatorname{LGr}(V)$}
{wiki}

The Lagrangian Grassmannian is the space of all <Lagrangian subspaces> of a symplectic vector space. The <unitary group> acts transitively on $\operatorname{LGr}(\mathbb R^{2n})$, and the stabilizer of $\mathbb R^n$ is the <orthogonal group> $O(n)$, giving
$$
\operatorname{LGr}(\mathbb R^{2n})\cong U(n)/O(n).
$$

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