Buildings of classical groups and centralizers of Lie algebra elements
| dc.creator | Broussous, P. | |
| dc.creator | Stevens, S. | |
| dc.date | 2004-02-13 | |
| dc.date.accessioned | 2026-07-07T05:05:26Z | |
| dc.date.available | 2026-07-07T05:05:26Z | |
| dc.description | Let F_o be a non-archimedean locally compact field of residual characteristic not 2. Let G be a classical group over F_o (with no quaternionic algebra involved) which is not of type A_n for n>1. Let b be an element of the Lie algebra g of G that we assume semisimple for simplicity. Let H be the centralizer of b in G and h its Lie algebra. Let I and I_b denote the (enlarged) Bruhat-Tits buildings of G and H respectively. We prove that there is a natural set of maps j_b : I_b --> I which enjoy the following properties: they are affine, H-equivariant, map any apartment of I_b into an apartment of I and are compatible with the Lie algebra filtrations of g and h. In a particular case, where this set is reduced to one element, we prove that j_b is characterized by the last property in the list. We also prove a similar characterization result for the general linear group. | |
| dc.description | 21 pages. Preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0402228 | |
| dc.identifier | http://arxiv.org/abs/math/0402228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70163 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.subject | 11E57; 11E95; 20E42; 51E24; 57S25 | |
| dc.title | Buildings of classical groups and centralizers of Lie algebra elements | |
| dc.type | text |