Timeline for length function of a coxeter group with respect to two different simple systems are equal or not?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2012 at 4:32 | vote | accept | Rekha Biswal | ||
| Dec 3, 2012 at 19:51 | answer | added | Jim Humphreys | timeline score: 3 | |
| Dec 3, 2012 at 15:38 | comment | added | paul garrett | As David Speyer notes, this can't be so, for fairly obvious reasons. But one's feeling that there is some "metric object" that is independent of generators is correct, namely, the "gallery-distance" on the associated Coxeter complex. The word-length is the gallery-distance from the distinguished chamber (reflections through whose sides are the given generators), to its image under the word. | |
| Dec 3, 2012 at 15:20 | vote | accept | Rekha Biswal | ||
| Dec 4, 2012 at 4:32 | |||||
| Dec 3, 2012 at 14:55 | answer | added | David E Speyer | timeline score: 4 | |
| Dec 3, 2012 at 14:29 | comment | added | Lee Mosher | I'm a little unclear on what you are asking (because I do not know what a "simple system" is), but here is a general fact. Given a group $W$ with two finite generating sets $S_1,S_2$ and their associated length functions $L_1$ and $L_2$, if $K$ is the maximum of $L_1(s), L_2(s)$ over all $s \in S_1 \cup S_2$ then $L_1(w)/K \le L_2(w) \le K L_1(w)$ for all $w \in W$. | |
| Dec 3, 2012 at 13:54 | history | asked | Rekha Biswal | CC BY-SA 3.0 |