Broussous, Paul and Stevens, Shaun (2009) Buildings of classical groups and centralizers of Lie algebra elements. Journal of Lie Theory, 19 (1). pp. 5578.
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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 
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:  16 May 2023 00:13 
URI:  https://ueaeprints.uea.ac.uk/id/eprint/21079 
DOI: 
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