Buildings of classical groups and centralizers of Lie algebra elements

dc.creatorBroussous, P.
dc.creatorStevens, S.
dc.date2004-02-13
dc.date.accessioned2026-07-07T05:05:26Z
dc.date.available2026-07-07T05:05:26Z
dc.descriptionLet F_o be a non-archimedean locally compact field of residual characteristic not 2. Let G be a classical group over F_o (with no quaternionic algebra involved) which is not of type A_n 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 I_b denote the (enlarged) Bruhat-Tits buildings of G and H respectively. We prove that there is a natural set of maps j_b : I_b --> I which enjoy the following properties: they are affine, H-equivariant, map any apartment of I_b 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 j_b is characterized by the last property in the list. We also prove a similar characterization result for the general linear group.
dc.description21 pages. Preliminary version
dc.identifierhttps://arxiv.org/abs/math/0402228
dc.identifierhttp://arxiv.org/abs/math/0402228
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70163
dc.subjectGroup Theory
dc.subjectRings and Algebras
dc.subject11E57; 11E95; 20E42; 51E24; 57S25
dc.titleBuildings of classical groups and centralizers of Lie algebra elements
dc.typetext

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