Reference request: Grassmannian and Plucker coordinates in type B, C, D The Next CEO of Stack OverflowInfinite Grassmannians and their coordinate ringsReference request: representation of type G2 Lie algebras.Borel–Weil theorem - reference requestRelations between affine Grassmannian and GrassmannianSubspaces of Grassmannian under Plucker embeddingLattice model for Affine Grassmannians of non type ADo we have super Plucker relations for a super Grassmannian?Reference request: type C, D Catalan numbersReference request: Catalan number of type BDecomposition of product of two Plucker coordinates
Reference request: Grassmannian and Plucker coordinates in type B, C, D
The Next CEO of Stack OverflowInfinite Grassmannians and their coordinate ringsReference request: representation of type G2 Lie algebras.Borel–Weil theorem - reference requestRelations between affine Grassmannian and GrassmannianSubspaces of Grassmannian under Plucker embeddingLattice model for Affine Grassmannians of non type ADo we have super Plucker relations for a super Grassmannian?Reference request: type C, D Catalan numbersReference request: Catalan number of type BDecomposition of product of two Plucker coordinates
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Grassmannian $Gr(k,n)$ is the set of $k$-dimensional subspace of an $n$-dimensional vector space. What are the Grassmannian in types B, C, D? What are the analog of Plucker coordinates and Plucker relations in these cases? Are there some references about this? Thank you very much.
ag.algebraic-geometry co.combinatorics rt.representation-theory lie-groups
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
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add a comment |
$begingroup$
Grassmannian $Gr(k,n)$ is the set of $k$-dimensional subspace of an $n$-dimensional vector space. What are the Grassmannian in types B, C, D? What are the analog of Plucker coordinates and Plucker relations in these cases? Are there some references about this? Thank you very much.
ag.algebraic-geometry co.combinatorics rt.representation-theory lie-groups
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
$endgroup$
add a comment |
$begingroup$
Grassmannian $Gr(k,n)$ is the set of $k$-dimensional subspace of an $n$-dimensional vector space. What are the Grassmannian in types B, C, D? What are the analog of Plucker coordinates and Plucker relations in these cases? Are there some references about this? Thank you very much.
ag.algebraic-geometry co.combinatorics rt.representation-theory lie-groups
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
$endgroup$
Grassmannian $Gr(k,n)$ is the set of $k$-dimensional subspace of an $n$-dimensional vector space. What are the Grassmannian in types B, C, D? What are the analog of Plucker coordinates and Plucker relations in these cases? Are there some references about this? Thank you very much.
ag.algebraic-geometry co.combinatorics rt.representation-theory lie-groups
ag.algebraic-geometry co.combinatorics rt.representation-theory lie-groups
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
asked 1 hour ago
Jianrong LiJianrong Li
2,47721318
2,47721318
add a comment |
add a comment |
1 Answer
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In type $B$ and $D$ these are orthogonal isotropic Grassmannians $$OGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate quadratic form.
In type $C$ these are symplectic isotropic Grassmannians $$SGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate symplectic form.
answered 37 mins ago
SashaSasha
21.2k22755
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$begingroup$
In type $B$ and $D$ these are orthogonal isotropic Grassmannians $$OGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate quadratic form.
In type $C$ these are symplectic isotropic Grassmannians $$SGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate symplectic form.
answered 37 mins ago
SashaSasha
21.2k22755
$endgroup$
add a comment |
$begingroup$
In type $B$ and $D$ these are orthogonal isotropic Grassmannians $$OGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate quadratic form.
In type $C$ these are symplectic isotropic Grassmannians $$SGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate symplectic form.
answered 37 mins ago
SashaSasha
21.2k22755
$endgroup$
add a comment |
$begingroup$
In type $B$ and $D$ these are orthogonal isotropic Grassmannians $$OGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate quadratic form.
In type $C$ these are symplectic isotropic Grassmannians $$SGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate symplectic form.
answered 37 mins ago
SashaSasha
21.2k22755
$endgroup$
In type $B$ and $D$ these are orthogonal isotropic Grassmannians $$OGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate quadratic form.
In type $C$ these are symplectic isotropic Grassmannians $$SGr(k,n) subset Gr(k,n),$$ that parameterize isotropic $k$-dimensional subspaces in a vector space of dimension $n$ endowed with a non-degenerate symplectic form.
answered 37 mins ago
SashaSasha
21.2k22755
answered 37 mins ago
SashaSasha
21.2k22755
answered 37 mins ago
SashaSasha
21.2k22755
answered 37 mins ago
SashaSasha
21.2k22755
21.2k22755
add a comment |
add a comment |
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