Buildings of classical groups and centralizers of Lie algebra elements

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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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
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
Faculty of Science > Research Groups > Number Theory (former - to 2017)
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Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:44
Last Modified: 16 May 2023 00:13


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