Timeline for Equivariant coherent sheaf category for unipotent group actions
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2021 at 17:52 | comment | added | Amanda Taylor | @WillSawin: I see. Thanks! | |
| Apr 1, 2021 at 17:26 | comment | added | Will Sawin | I thought it should just be the $U$-equivariant space, but then I realized that the cohomology should probably also involve the $U$-cohomology of the Borel-Weil-Bott Ext-space (which is itself the Ext of the constant representation by that representation in the category of $U$-representations) and thus might be a bit more complicated. | |
| Apr 1, 2021 at 17:17 | comment | added | Amanda Taylor | @WillSawin: Dear Will, thanks for your comments! Maybe I will first try to calculate the U-equivariant morphisms between the line bundles as you suggested. Is it true that the $U$-invariant space in $Ext^i(\mathcal{L}(\lambda), \mathcal{L}(\mu))$ (using Borel-Weil-Bott) calculates the $U$-equivariant morphisms? Or the latter is more complicated than that? | |
| Apr 1, 2021 at 4:09 | comment | added | Will Sawin | The structure sheaves of the closures of strata have a natural $U$-equivariant structure, and they should generate, but I don't know how to calculate the homomorphisms. The line bundles on $G/B$ have a $G$-equivariant structure, hence $G/B$-equivariant, and you can probably calculate the $U$-equivariant homomorphisms from Borel-Weil-Bott, but it's not obvious to me how to choose a subset that generates. | |
| Apr 1, 2021 at 3:05 | review | First posts | |||
| Apr 1, 2021 at 6:09 | |||||
| Apr 1, 2021 at 3:03 | history | asked | Amanda Taylor | CC BY-SA 4.0 |