Timeline for Fixed Points of the Weyl Group action on a Maximal Torus and the Center of a Reductive Group
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Aug 19, 2018 at 17:39 | comment | added | Alexander | @Jim_Humphreys Ok, then I guess I'm not understanding what you are upset about. To my eyes, the title of my question clearly reflects its contents. I'd appreciate some clarification. Best wishes | |
| Aug 18, 2018 at 23:36 | comment | added | Jim Humphreys | @Alexander: The minor changes to your header are too weak, so I'll stick with my own answer. | |
| Aug 15, 2018 at 18:42 | comment | added | Alexander | @Jim_Humphreys Ok thanks for the feedback. I hope the changes I have made are an improvement. | |
| Aug 15, 2018 at 14:54 | comment | added | Jim Humphreys | @Alexander: It's probably useful even at this point to revise your header and the inadequate subject tags. For example, "Weyl [group] invariants" basically have nothing to do with the actual question. The invariants were actually worked out by Chevalley. Note too that you are concerned with algebraic groups (in practice semisimple) over number fields of characteristic 0. (So a tag 'nt.nunber-theory' would perhaps be appropriate.) | |
| S Aug 12, 2018 at 1:22 | history | suggested | Alexander | CC BY-SA 4.0 |
fixed typos
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| Aug 12, 2018 at 0:27 | comment | added | Alexander | The $\Gamma$ invariants are not in the center for the reason discussed above. So even if it's not a natural question, it happened to be relevant! | |
| Aug 12, 2018 at 0:25 | comment | added | Alexander | Dear Prof. Humphreys, The question arose because a friend and I happened to be interested in the following situation. One has a reductive group $G$ defined over a number field $F$ with maximal torus $T$ and one wants to understand when the Galois invariants of the complex dual torus $\hat{T}^{\Gamma}$ are contained within $Z(\hat{G})$. In the case where $G$ is split, we concluded that the $\Gamma$-action on $\hat{T}$ factors through the Weyl action. Therefore in the particular case where $G=SL_2$, so that $\hat{G}= PGL_2$ and $T$ is an anisotropic maximal torus | |
| Aug 11, 2018 at 23:49 | review | Suggested edits | |||
| S Aug 12, 2018 at 1:22 | |||||
| Aug 11, 2018 at 18:54 | history | answered | Jim Humphreys | CC BY-SA 4.0 |