Timeline for Bruhat decomposition for G(R), R local ring or R=Z/p^r
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2011 at 17:30 | comment | added | paul garrett | Despite the difficulty of the problem as posed, there is still the Iwahori version, that $G(\mathbb Z_p)=JWJ$ (disjoint union!), where $J$ is Iwahori, $W$ is the spherical Weyl group. The disjointness of the union sometimes reduces what is otherwise reasonably perceived as fairly chaotic. | |
| Mar 11, 2011 at 10:33 | vote | accept | Marc Palm | ||
| Mar 10, 2011 at 1:02 | comment | added | Amritanshu Prasad | Thanks for the helpful comment Jim. I would be happy to send a copy of the published version to anyone who requests it. | |
| Mar 9, 2011 at 17:58 | comment | added | Jim Humphreys | There have been earlier attempts by people working in algebraic K-theory to exploit Bruhat decomposition over rings and ideals, including early work by M.R. Stein; but that work is probably not close enough to the precise question asked here. (By the way, it's useful to note that the cited paper is available at arXiv, since our library and many others long ago found the journal unaffordable.) | |
| Mar 9, 2011 at 10:28 | comment | added | Amritanshu Prasad | We did $n=3$ explicitly. At least there $p$ enters the picture in a very controlled way. In general, it seems like there should some hidden structure which we do not understand. | |
| Mar 9, 2011 at 10:02 | comment | added | Marc Palm | Thanks for the fast response. So, I guess the quotient $B\GL_n/B$ is pretty nasty and not an algebraic variety? | |
| Mar 9, 2011 at 8:18 | history | answered | Amritanshu Prasad | CC BY-SA 2.5 |