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
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2012 at 4:32 | vote | accept | Rekha Biswal | ||
| Dec 4, 2012 at 4:32 | comment | added | Rekha Biswal | @Jim actually the question is as follows,how the length function of elements of weyl group are related with respect to two different simple systems? | |
| Dec 3, 2012 at 21:00 | comment | added | Misha | @Jim: Things are actually even more interesting, since one can have two Coxeter systems $(W_1,S_1), (W_2,S_2)$, where $W_1$ is isomorphic to $W_2$ as an abstract group, but that there is no isomorphism of Coxeter systems. Thus, the entire premise of $S_1$ being conjugate to $S_2$ is false. On the other hand, in many cases, Coxeter groups are "rigid", see e.g. perso.uclouvain.be/pierre-emmanuel.caprace/papers_pdf/… | |
| Dec 3, 2012 at 19:51 | history | answered | Jim Humphreys | CC BY-SA 3.0 |