Timeline for Weyl group of the restriction of scalars of split reductive group
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2013 at 19:18 | answer | added | Jim Humphreys | timeline score: 5 | |
| Apr 30, 2013 at 22:58 | comment | added | Arkandias | Thank you nosr. If you could post your answer so I can accept it. | |
| Apr 30, 2013 at 17:09 | comment | added | Marc Palm | nosr. please put this as answer. | |
| Apr 30, 2013 at 15:37 | comment | added | user28172 | [I assume when you wrote "maximal (split) torus" you mean that $T$ is a split maximal $E$-torus of $G$ that is also maximal as an $E$-torus.] | |
| Apr 30, 2013 at 15:35 | comment | added | user28172 | They're equal. This can be seen in multiple ways. For example, the evident isomorphism $S'_E \rightarrow T$ induced by $G_{E'} \twoheadrightarrow G$ gives an identification ${\rm{X}}_F(S') = {\rm{X}}_F(T)$ under which $\Phi(G',S')$ is carried isomorphically onto $\Phi(G,T)$ (using the equality of $\mathfrak{g}'$ with the underlying $F$-vector space of $\mathfrak{g}$ to match root spaces), and the Weyl group of this common root system is naturally identified with the finite constant groups $W$ and $W'$. This respects the induced map $W'_E \rightarrow W$, so the latter is an isomorphism. | |
| Apr 30, 2013 at 14:35 | history | asked | Arkandias | CC BY-SA 3.0 |