Broussous, Paul and Stevens, Shaun (2009) Buildings of classical groups and centralizers of Lie algebra elements. Journal of Lie Theory, 19 (1). pp. 5578.
Other (building.dvi)
Download (97kB) 

Preview 
PDF (building.pdf)
 Accepted Version
Download (217kB)  Preview 
Abstract
Let Fo be a nonarchimedean 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) BruhatTits 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, Hequivariant, 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 (former  to 2024) 
UEA Research Groups:  Faculty of Science > Research Groups > Algebra and Combinatorics Faculty of Science > Research Groups > Number Theory (former  to 2017) 
Related URLs:  
Depositing User:  Vishal Gautam 
Date Deposited:  18 Mar 2011 14:44 
Last Modified:  06 Sep 2024 00:00 
URI:  https://ueaeprints.uea.ac.uk/id/eprint/21079 
DOI: 
Downloads
Downloads per month over past year
Actions (login required)
View Item 