Timeline for Are there infinite abelian real reflection groups?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2021 at 12:51 | vote | accept | Martin Skilleter | ||
| Sep 9, 2021 at 12:49 | comment | added | Johannes Hahn | The same argument put more succinctly: The generating reflections are diagonalisable over $\mathbb{R}$ (because they're reflections) and commute by assumption. Therefore they are simultaneously diagonalisable, i.e. they are conjugated to a subgroup of $\{\pm 1\}^n$ which is finite. EDIT: Martin was a few seconds faster. | |
| Sep 9, 2021 at 12:48 | comment | added | Martin Skilleter | Is the fact that $V$ is $G$-invariant simply because reflections are diagonalisable, and commuting diagonalisable operators can be simultaneously diagonalised? I can't see anywhere else you are using the abelian hypothesis. | |
| Sep 9, 2021 at 12:30 | history | answered | Geoff Robinson | CC BY-SA 4.0 |