Broussous, Paul and Stevens, Shaun (2009) Buildings of classical groups and centralizers of Lie algebra elements. Journal of Lie Theory, 19 (1). pp. 55-78.
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Abstract
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 |
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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: |
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