Timeline for Buildings associated to generalized $BN$ pairs
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 13, 2015 at 15:29 | vote | accept | John Binder | ||
| Mar 13, 2015 at 13:42 | answer | added | Paul Broussous | timeline score: 4 | |
| Jan 13, 2015 at 16:50 | comment | added | LSpice | A vertex $g\operatorname{GL}_2(\mathbb Z_p)$ should be identified with the maximal parahoric subgroup $g\operatorname{GL}_2(\mathbb Z_p)g^{-1}$. Two such parahorics are adjacent if their intersection is an Iwahori subgroup of each. (For example, $\operatorname{GL}_2(\mathbb Z_p)$ is adjacent to its conjugate by $\begin{pmatrix} p & 0 \\ 0 & 1 \end{pmatrix}$.) | |
| Jan 13, 2015 at 16:11 | comment | added | John Binder | @LSpice thanks for the comment; Rabinoff's notes are indeed excellent. Could you please expand on the graph structure of the enlarged building of $GL_2(\mathbb{Q}_p)$? I must be missing the identification between the set of vertices and $GL_2(\mathbb{Q}_p)/GL_2(\mathbb{Z}_p)$. | |
| Jan 12, 2015 at 21:40 | comment | added | LSpice | Also, the (enlarged) building of $\operatorname{GL}_2(\mathbb Q_p)$ is indeed 1-dimensional, but its set of vertices is $\operatorname{GL}_2(\mathbb Q_p)/\operatorname{GL}_2(\mathbb Z_p)$. There is a very nice senior thesis by Joe Rabinoff at people.math.gatech.edu/~jrabinoff6/papers/building.pdf, describing all this in modern and very accessible language. | |
| Jan 12, 2015 at 21:36 | comment | added | LSpice | The 'enlarged building' associated to a reductive group is just the building of its derived group, times an affine space under the (real-ified) cocharacters of the centre. | |
| Jan 12, 2015 at 19:46 | history | asked | John Binder | CC BY-SA 3.0 |