Timeline for Drinfeld Sokolov and the semiinfinite flag variety
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 15, 2021 at 21:44 | comment | added | Pulcinella | I'd be very interested in seeing what's been published, especially for the semiinfinite flag variety (or the affine grassmannian, or the affine flag variety). I'm actually interested in non-critical level, but I suppose understanding the critical level will help hugely nonetheless. | |
| Mar 13, 2021 at 3:55 | comment | added | dhy | @Meow This is a very deep question, and a bunch of work (not all published) has been done on it for different values of $X$. I don't know of any individual such $X$ that "best approximates" $\hat{g}\operatorname{-mod}$, but by studying the map for different values of $X$ one can learn a huge amount about $\hat{g}\operatorname{-mod}.$ If you name a specific $X$ you are curious about I can tell you what is known (at least at critical level, where the story is a bit more straightforward). | |
| Mar 12, 2021 at 21:18 | comment | added | Pulcinella | Thanks, this is a really wonderful answer! I suppose my question about the semiinfinite flag variety might be: is there a special space $X$ with an $\widehat{LG}$ action for which the map $\text{Whit}(D(X))\to\text{Whit}(\hat{g}\text{-mod})$ an isomorphism, or close to one? Basically whether for a certain space $X$ your "slightly silly application" is maximally nice. | |
| Mar 12, 2021 at 21:10 | vote | accept | Pulcinella | ||
| Mar 11, 2021 at 18:06 | history | answered | dhy | CC BY-SA 4.0 |