Timeline for Does an affine building associated to a group satisfy the axioms of building?
Current License: CC BY-SA 4.0
9 events
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| Sep 29, 2022 at 16:46 | history | edited | LSpice | CC BY-SA 4.0 |
Link; formatting; TeX -> Unicode quotes
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| Sep 29, 2022 at 16:43 | answer | added | LSpice | timeline score: 4 | |
| Sep 29, 2022 at 14:49 | comment | added | M masa | Sorry. I did not explain the strong transitivity. Let $\mathcal{A}$ be a system of apartments, now in this case, $\mathcal{A}=\{gA\mathrel{\vert}g\in G\}$. We say that the action of $G$ is strongly transitive if for any $A_{1},A_{2}\in \mathcal{A}$ and chambers $C_{1}\subset A_{1}, C_{2}\subset A_{2}$, there exists $g\in G$ such that $g(A_{1},C_{1})=(A_{2},C_{2})$. | |
| Sep 29, 2022 at 13:44 | comment | added | LSpice | $N = N_G(T)$, I guess. (1) is true, and is almost certainly in both BT1 which you are reading, and in Tits's Corvallis article which is much more accessible. Is "strong transitivity" in (2) the requirement of transitivity on finite subsets of the same cardinality? This is certainly not true; the action of $G$ is not even transitive on points. So perhaps you want transitivity on finite sets of vertices, maybe with some distance condition? That, too, can fail, again even for single vertices, even if $G$ is adjoint, in special cases. | |
| Sep 29, 2022 at 12:27 | history | edited | YCor | CC BY-SA 4.0 |
formatting, fixed English
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| Sep 29, 2022 at 12:13 | comment | added | Carl-Fredrik Nyberg Brodda | @YCor And with the singular "root datum". | |
| Sep 29, 2022 at 11:57 | history | edited | M masa | CC BY-SA 4.0 |
deleted 12 characters in body
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| Sep 29, 2022 at 10:49 | comment | added | YCor | I think that the standard English translation of the French "données radicielles" is "root data" | |
| Sep 29, 2022 at 10:43 | history | asked | M masa | CC BY-SA 4.0 |