Buildings of classical groups and centralizers of Lie algebra elements

Broussous, P and Stevens, S (2009) Buildings of classical groups and centralizers of Lie algebra elements. Journal of Lie Theory, 19 (1). pp. 55-78.

[thumbnail of building.dvi] Other (building.dvi)
Download (97kB)
[thumbnail of building.pdf]
PDF (building.pdf)
Download (217kB) | Preview


Let Fo be a non-archimedean locally compact field of residual characteristic not 2. Let G be a classical group over Fo (with no quaternionic algebra involved) which is not of type An 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 Ib denote the (enlarged) Bruhat-Tits buildings of G and H respectively. We prove that there is a natural set of maps jb : Ib ? I which enjoy the following properties: they are affine, H-equivariant, map any apartment of Ib 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 jb is characterized by the last property in the list. We also prove a similar characterization result for the general linear group.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 23 Oct 2022 01:53

Actions (login required)

View Item View Item