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YCor
YCor
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Reference request: Grassmannian $Gr$\mathrm{Gr}(k, \pm \infty)$ in infinite dimension

The$\DeclareMathOperator\Gr{Gr}$The Grassmnnian variety $Gr(k,n)$$\Gr(k,n)$ is the set of $k$-dimensional subspaces of $\mathbb{C}^n$. The coordinate ring $\mathbb{C}[Gr(k,n)]$$\mathbb{C}[\Gr(k,n)]$ is generated by Plucker coordinates subject to Plucker relations.

Denote by $Gr(k, \pm \infty)$$\Gr(k, \pm \infty)$ the set of $k$-dimensional subspaces of $\mathbb{C}^{\infty}$. The coordinate ring $\mathbb{C}[Gr(k,\pm \infty)]$$\mathbb{C}[\Gr(k,\pm \infty)]$ is generated by Plucker coordinates $P_J$, $J \subset \mathbb{Z}$, subject to Plucker relations. Has $\mathbb{C}[Gr(k,\pm \infty)]$$\mathbb{C}[\Gr(k,\pm \infty)]$ been defined in the literature? Thank you very much.

Reference request: Grassmannian $Gr(k, \pm \infty)$

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 coordinates subject to Plucker relations.

Denote by $Gr(k, \pm \infty)$ the set of $k$-dimensional subspaces of $\mathbb{C}^{\infty}$. The coordinate ring $\mathbb{C}[Gr(k,\pm \infty)]$ is generated by Plucker coordinates $P_J$, $J \subset \mathbb{Z}$, subject to Plucker relations. Has $\mathbb{C}[Gr(k,\pm \infty)]$ been defined in the literature? Thank you very much.

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 coordinates subject to Plucker relations.

Denote by $\Gr(k, \pm \infty)$ the set of $k$-dimensional subspaces of $\mathbb{C}^{\infty}$. The coordinate ring $\mathbb{C}[\Gr(k,\pm \infty)]$ is generated by Plucker coordinates $P_J$, $J \subset \mathbb{Z}$, subject to Plucker relations. Has $\mathbb{C}[\Gr(k,\pm \infty)]$ been defined in the literature? Thank you very much.

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Jianrong Li
Jianrong Li
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Reference request: Grassmannian $Gr(k, \pm \infty)$

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 coordinates subject to Plucker relations.

Denote by $Gr(k, \pm \infty)$ the set of $k$-dimensional subspaces of $\mathbb{C}^{\infty}$. The coordinate ring $\mathbb{C}[Gr(k,\pm \infty)]$ is generated by Plucker coordinates $P_J$, $J \subset \mathbb{Z}$, subject to Plucker relations. Has $\mathbb{C}[Gr(k,\pm \infty)]$ been defined in the literature? Thank you very much.