Timeline for What is a canonical set of representatives in $GL(n,F)$ for the vertices in the Bruhat Tits building?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 17, 2011 at 12:53 | vote | accept | Marc Palm | ||
| Dec 15, 2011 at 9:35 | comment | added | Marc Palm | Nevertheless, it is certainly solved somewhere. The final partition looks like $$ \coprod\limits_{\alpha_1 \in T(F) / T(o)} \coprod\limits_{\alpha_2 \in E_1(F) / E_1(o)^{\alpha_{1}} } \cdots \coprod\limits_{E_n(F) / E_n(o)^{\alpha_1 \alpha_2 \cdots \alpha_{n-1}}},$$ where $E_k$ is the set of upper diagonal matrices with only $k-th$ column nonzero and $H^x = x^{-1} H x$. | |
| Dec 15, 2011 at 9:18 | comment | added | Marc Palm | That was my initial idea too. I have now succeeded by iterating your argument also for the unipotent radical, seen as an iterated semidirect product. Thanks. | |
| Dec 14, 2011 at 20:14 | comment | added | Paul Broussous | Here $O={\mathfrak o}$ is the ring of integers, and $\varpi$ a uniformizer. | |
| Dec 14, 2011 at 20:13 | history | answered | Paul Broussous | CC BY-SA 3.0 |