Reference request: additive basis of coordinate ring of GrassmanniansInfinite Grassmannians and their coordinate ringsReference Request: Riemann's Existence TheoremUniversal etale covering, reference requestDieudonné modules -reference requestReal plane cubic curves from points in Gr(3,6) via a certain 6x6 determinantetale localization reference requestZariski density reference requestAn $F$-open set, which is affine, is an affine $F$-varietyTangent space of Grassmannians on Mukai's bookExplicit form of raising and lowering operators in spherical gl(n) DAHA
Reference request: additive basis of coordinate ring of Grassmannians
Infinite Grassmannians and their coordinate ringsReference Request: Riemann's Existence TheoremUniversal etale covering, reference requestDieudonné modules -reference requestReal plane cubic curves from points in Gr(3,6) via a certain 6x6 determinantetale localization reference requestZariski density reference requestAn $F$-open set, which is affine, is an affine $F$-varietyTangent space of Grassmannians on Mukai's bookExplicit form of raising and lowering operators in spherical gl(n) DAHA
$begingroup$
Let $tildeGr(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $mathbbC[tildeGr(k,n)]$:
beginalign
S = e_T: T text is a rectangular semi-standard Young tableau with $k$ rows,
endalign
where $e_T = P_T_1 cdots P_T_n$, where $T_i$'s are columns of $T$ and $P_T_i$ is the Plücker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.
ag.algebraic-geometry
edited 2 days ago
Michael Albanese
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
$endgroup$
add a comment |
$begingroup$
Let $tildeGr(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $mathbbC[tildeGr(k,n)]$:
beginalign
S = e_T: T text is a rectangular semi-standard Young tableau with $k$ rows,
endalign
where $e_T = P_T_1 cdots P_T_n$, where $T_i$'s are columns of $T$ and $P_T_i$ is the Plücker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.
ag.algebraic-geometry
edited 2 days ago
Michael Albanese
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
$endgroup$
add a comment |
$begingroup$
Let $tildeGr(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $mathbbC[tildeGr(k,n)]$:
beginalign
S = e_T: T text is a rectangular semi-standard Young tableau with $k$ rows,
endalign
where $e_T = P_T_1 cdots P_T_n$, where $T_i$'s are columns of $T$ and $P_T_i$ is the Plücker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.
ag.algebraic-geometry
edited 2 days ago
Michael Albanese
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
$endgroup$
Let $tildeGr(k,n)$ be the affine cone of the Grassmannian $Gr(k,n)$. I think that the following set $S$ is an additive basis of $mathbbC[tildeGr(k,n)]$:
beginalign
S = e_T: T text is a rectangular semi-standard Young tableau with $k$ rows,
endalign
where $e_T = P_T_1 cdots P_T_n$, where $T_i$'s are columns of $T$ and $P_T_i$ is the Plücker with indices from the entries of $T_i$. Are there some references about this? Thank you very much.
ag.algebraic-geometry
ag.algebraic-geometry
edited 2 days ago
Michael Albanese
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
edited 2 days ago
Michael Albanese
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
edited 2 days ago
Michael Albanese
8,03055594
edited 2 days ago
Michael Albanese
8,03055594
edited 2 days ago
Michael Albanese
8,03055594
8,03055594
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
asked May 4 at 15:15
Jianrong LiJianrong Li
2,56721319
2,56721319
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The result you mention is very classical, but it also fits within the more general and conceptual framework of Standard Monomial Theory: https://en.wikipedia.org/wiki/Standard_monomial_theory.
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
$endgroup$
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
add a comment |
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1 Answer
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active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The result you mention is very classical, but it also fits within the more general and conceptual framework of Standard Monomial Theory: https://en.wikipedia.org/wiki/Standard_monomial_theory.
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
$endgroup$
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
add a comment |
$begingroup$
The result you mention is very classical, but it also fits within the more general and conceptual framework of Standard Monomial Theory: https://en.wikipedia.org/wiki/Standard_monomial_theory.
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
$endgroup$
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
add a comment |
$begingroup$
The result you mention is very classical, but it also fits within the more general and conceptual framework of Standard Monomial Theory: https://en.wikipedia.org/wiki/Standard_monomial_theory.
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
$endgroup$
The result you mention is very classical, but it also fits within the more general and conceptual framework of Standard Monomial Theory: https://en.wikipedia.org/wiki/Standard_monomial_theory.
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
answered May 4 at 15:17
Sam HopkinsSam Hopkins
5,50212561
5,50212561
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
add a comment |
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
$begingroup$
thank you very much. I am trying to find an explicit place of the result. But I could not find it. Is there a more explicit reference? Thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:30
1
1
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
@JianrongLi: See for instance Chapter 1 of Seshadri's "Introduction to the Theory of Standard Monomials" (springer.com/us/book/9789811018138) which covers the Grassmannian.
$endgroup$
– Sam Hopkins
May 4 at 16:44
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
$begingroup$
thank you very much.
$endgroup$
– Jianrong Li
May 4 at 16:45
add a comment |
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