Reference Request for $fracGB rightarrow fracGP$ being a fiber bundle for $G = GL_n(mathbbC)$ The 2019 Stack Overflow Developer Survey Results Are InIntersection of the Irreducible Components of Intersections of Schubert VarietiesConstruction of line bundles on the flag varietyReference request for studying on Fiber bundlesClarifications about parabolic subgroups of $GL_4$Borel-Weil-Bott Theorem stepA certain generalization of flag varietiesMost general definition of Borel and parabolic Lie algebras?Is the quotient of standard parabolic subgroups isomorphic to a Schubert varietyNormalisers and connectedness of parabolic subgroupsSingular Schubert Variety in $Fl_4(mathbb C)$
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Reference Request for $fracGB rightarrow fracGP$ being a fiber bundle for $G = GL_n(mathbbC)$
The 2019 Stack Overflow Developer Survey Results Are InIntersection of the Irreducible Components of Intersections of Schubert VarietiesConstruction of line bundles on the flag varietyReference request for studying on Fiber bundlesClarifications about parabolic subgroups of $GL_4$Borel-Weil-Bott Theorem stepA certain generalization of flag varietiesMost general definition of Borel and parabolic Lie algebras?Is the quotient of standard parabolic subgroups isomorphic to a Schubert varietyNormalisers and connectedness of parabolic subgroupsSingular Schubert Variety in $Fl_4(mathbb C)$
$begingroup$
Let $G = GL_n(mathbbC)$, let $B$ be the Borel subgroup of upper triangular matrices, and let $P$ be a parabolic subgroup. Then we may identify $G/B$ with the complete flag variety and $G/P$ with the partial flag variety. I am looking for a reference for a proof that the map sending $gB to gP$ is a fiber bundle and would appreciate any help.
I have looked through multiple lecture notes, papers, and textbooks and the best that I have been able to find are these lecture notes by Michael Brion. Between my advisor and these resources I've gathered that the preimage of a Schubert cell $BwP/P subset G/P$ should be isomorphic to the Schubert cell and the products of complete flag varieties, but I have been unable to find a resource which contains a proof of this. Any and all help would be much appreciated, thank you very much.
algebraic-geometry reference-request representation-theory algebraic-groups fiber-bundles
asked Apr 6 at 20:14
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$begingroup$
Let $G = GL_n(mathbbC)$, let $B$ be the Borel subgroup of upper triangular matrices, and let $P$ be a parabolic subgroup. Then we may identify $G/B$ with the complete flag variety and $G/P$ with the partial flag variety. I am looking for a reference for a proof that the map sending $gB to gP$ is a fiber bundle and would appreciate any help.
I have looked through multiple lecture notes, papers, and textbooks and the best that I have been able to find are these lecture notes by Michael Brion. Between my advisor and these resources I've gathered that the preimage of a Schubert cell $BwP/P subset G/P$ should be isomorphic to the Schubert cell and the products of complete flag varieties, but I have been unable to find a resource which contains a proof of this. Any and all help would be much appreciated, thank you very much.
algebraic-geometry reference-request representation-theory algebraic-groups fiber-bundles
asked Apr 6 at 20:14
PQ-PQ-
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Let $G = GL_n(mathbbC)$, let $B$ be the Borel subgroup of upper triangular matrices, and let $P$ be a parabolic subgroup. Then we may identify $G/B$ with the complete flag variety and $G/P$ with the partial flag variety. I am looking for a reference for a proof that the map sending $gB to gP$ is a fiber bundle and would appreciate any help.
I have looked through multiple lecture notes, papers, and textbooks and the best that I have been able to find are these lecture notes by Michael Brion. Between my advisor and these resources I've gathered that the preimage of a Schubert cell $BwP/P subset G/P$ should be isomorphic to the Schubert cell and the products of complete flag varieties, but I have been unable to find a resource which contains a proof of this. Any and all help would be much appreciated, thank you very much.
algebraic-geometry reference-request representation-theory algebraic-groups fiber-bundles
asked Apr 6 at 20:14
PQ-PQ-
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Let $G = GL_n(mathbbC)$, let $B$ be the Borel subgroup of upper triangular matrices, and let $P$ be a parabolic subgroup. Then we may identify $G/B$ with the complete flag variety and $G/P$ with the partial flag variety. I am looking for a reference for a proof that the map sending $gB to gP$ is a fiber bundle and would appreciate any help.
I have looked through multiple lecture notes, papers, and textbooks and the best that I have been able to find are these lecture notes by Michael Brion. Between my advisor and these resources I've gathered that the preimage of a Schubert cell $BwP/P subset G/P$ should be isomorphic to the Schubert cell and the products of complete flag varieties, but I have been unable to find a resource which contains a proof of this. Any and all help would be much appreciated, thank you very much.
algebraic-geometry reference-request representation-theory algebraic-groups fiber-bundles
algebraic-geometry reference-request representation-theory algebraic-groups fiber-bundles
asked Apr 6 at 20:14
PQ-PQ-
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 6 at 20:14
PQ-PQ-
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 6 at 20:14
PQ-PQ-
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 6 at 20:14
PQ-PQ-
1
asked Apr 6 at 20:14
PQ-PQ-
1
1
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
PQ- is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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