Timeline for Invariants of the maximal unipotent subgroup of GL(n) acting on the space of n by n matrices
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2015 at 23:08 | comment | added | Raul Gomez | @JasonStarr You are right. Sorry it took me this long to digest your answer. | |
| Jul 24, 2015 at 23:01 | vote | accept | Raul Gomez | ||
| Jul 24, 2015 at 16:20 | answer | added | Jim Humphreys | timeline score: 2 | |
| Jul 24, 2015 at 2:50 | comment | added | Jason Starr | @RaulGomez. "What I'm looking for is a description of $\text{Spec} \ \mathbb{C}[X]^U$." Are you looking for a description as a subvariety $Z$ of an affine space? I gave that below: up to the $\mathbb{G}_m$-factor $Z^n$, $Z$ is just the affine cone over the flag variety. | |
| Jul 24, 2015 at 2:43 | comment | added | Raul Gomez | @Jason Sorry I was imprecise. What I'm looking for is a description of $\operatorname{Spec} \mathbb{C}[X]^{U}$ | |
| Jul 24, 2015 at 1:44 | answer | added | Jason Starr | timeline score: 8 | |
| Jul 23, 2015 at 23:07 | comment | added | Jason Starr | When you ask about the "categorical quotient", in what category, precisely, are you working? The categorical quotient in the category of schemes is not an affine scheme (just consider the case when $n$ equals $2$). You might want to look up "Matsushima's criterion" (extended to positive characteristic by Richardson). | |
| Jul 23, 2015 at 21:46 | comment | added | Raul Gomez | @WhatsUp Yes, it is the polynomial algebra. | |
| Jul 23, 2015 at 21:37 | comment | added | WhatsUp | Just for clarification: is $\mathbb{C}[X]$ the polynomial ring in $n^2$ variables? (It can be the group algebra as well...) And $\mathbb{C}[X]^U$ is the invariants under $U$? | |
| Jul 23, 2015 at 21:18 | history | asked | Raul Gomez | CC BY-SA 3.0 |