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Grassmannian $\mathrm{Gr}(k, \pm \infty)$ in infinite dimension
$\DeclareMathOperator\Gr{Gr}$The Grassmnnian variety $\Gr(k,n)$ is the set of $k$-dimensional subspaces of $\mathbb{C}^n$. The coordinate ring $\mathbb{C}[\Gr(k,n)]$ is generated by Plucker ...