Usbrth

How to manage monthly salary

Return to UK after being refused entry years previously

Are there any other methods to apply to solving simultaneous equations?

Falsification in Math vs Science

During Temple times, who can butcher a kosher animal?

What do hard-Brexiteers want with respect to the Irish border?

Deal with toxic manager when you can't quit

Is a "Democratic" Oligarchy-Style System Possible?

Shouldn't "much" here be used instead of "more"?

Pokemon Turn Based battle (Python)

Why do we hear so much about the Trump administration deciding to impose and then remove tariffs?

What does "fetching by region is not available for SAM files" means?

Is flight data recorder erased after every flight?

Should I use my personal e-mail address, or my workplace one, when registering to external websites for work purposes?

Button changing it's text & action. Good or terrible?

What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?

Can you compress metal and what would be the consequences?

Why was M87 targetted for the Event Horizon Telescope instead of Sagittarius A*?

Is there any way to tell whether the shot is going to hit you or not?

What tool would a Roman-age civilization have for the breaking of silver and other metals into dust?

Loose spokes after only a few rides

Where to refill my bottle in India?

Resizing object distorts it (Illustrator CC 2018)

Aging parents with no investments

Reference Request for $fracGB rightarrow fracGP$ being a fiber bundle for $G = GL_n(mathbbC)$

0

$begingroup$

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

share|cite|improve this question

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 | 

0

$begingroup$

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

share|cite|improve this question

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

share|cite|improve this question

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.

$endgroup$

share|cite|improve this question

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.

share|cite|improve this question

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