Timeline for Understanding the purely formal part of the sheaf theoretic (cohomological) framework for representation theory
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2016 at 10:56 | comment | added | Saal Hardali | @DavidBen-Zvi (Medium to High enthusiasm:) Is the monad in your statement the one you get from the composition of the push/pull (with some possible shrieks) adjunctions $BG \leftarrow BB \rightarrow BH$? (Very High enthsiasm) : "identification of that monad as a graded version of the Weyl group" Where can I find more about this?! I tried googling "Sam Gunningham" along with other stuff and nothing turned up. Finally I must confess I'm a die hard fan of yours, I can't thank you enough for all your insightful comments and answers on this site! | |
| Jul 24, 2016 at 1:10 | comment | added | David Ben-Zvi | Here and elsewhere W appears in the form of B\G/B, the self fiber product of BB over BG. BTW this formulation of BWB I learned from Sam Gunningham's thesis | |
| Jul 24, 2016 at 1:07 | comment | added | David Ben-Zvi | Here H= the torus, which you shouldn't consider as a subgroup of G but via the correspondence G <-- B --> H for B a Borel | |
| Jul 24, 2016 at 1:04 | comment | added | David Ben-Zvi | Yes Borel Weil Bott can be rewritten as the description of sheaves on BG as modules for a monad on BH, and the identification of that monad as a graded version of the Weyl group | |
| Jul 23, 2016 at 21:15 | comment | added | Saal Hardali | So is there a phrasing of Borel-Weil-Bott which says something like "the derived pushforward on coherent sheaves from $Coh((G/H)/G)$ to $Coh(pt/G)$ decsends to an equivalence of grothendiek groups or something similar in vane? (maybe weaker or stronger). | |
| Jul 23, 2016 at 21:11 | history | edited | Qiaochu Yuan | CC BY-SA 3.0 |
added 26 characters in body
|
| Jul 23, 2016 at 21:09 | comment | added | Qiaochu Yuan | @Saal: yes. It makes more sense if I write the quotient by $G$ on the left but I've forgotten how to do that in LaTeX. | |
| Jul 23, 2016 at 21:03 | comment | added | Saal Hardali | This is great stuff thanks! So the equivalence of stacks between $(G/H)/G$ and $pt/H$ is purely formal? | |
| Jul 21, 2016 at 18:21 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 |