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Grassmannians are algebraic varieties whose points corresponds to vector subspaces of a fixed dimension in a fixed vector space.

10 votes
2 answers
1k views

Relations between affine Grassmannian and Grassmannian

Let $\mathcal K = k((t))$ be the field of formal Laurent series over $k$, and by $\mathcal O = k[[t]]$ the ring of formal power series over $k$. Let $G$ be an algebraic group over $k$. The affine Gr …
Jianrong Li's user avatar
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5 votes
0 answers
213 views

Distance of two points in Grassmannian using Plücker coordinate

Let $G(q,D)$ be the Grassmannian of $q$-dimensional vector spaces in $\mathbb{R}^D$, where $q \le D$ are positive integers. In the paper, a distance between two points of $G(q,D)$ are defined as follo …
Jianrong Li's user avatar
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2 votes
0 answers
61 views

Multiplication formula in Grassmannian cluster categories

Grassmannian cluster categories are studied in A categorification of Grassmannian cluster algebras and Cluster categories from Grassmannians and root combinatorics. …
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2 votes
1 answer
242 views

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 coordinate …
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0 votes
0 answers
325 views

Relation between $3$-term Plücker relations and more than $3$-term Plücker relations

$\DeclareMathOperator\Gr{Gr}$Let $\Gr(k,n)$ be the Grassmannian variety of $k$-planes in an $n$-dimensional vector space. The coordinate algebra $\mathbb{C}[\Gr(k,n)]$ is generated by Plücker coordina …
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  • 6,201