An analogue of the Cartan decomposition for p-adic reductive symmetric spaces

dc.creatorDelorme, Patrick
dc.creatorSecherre, Vincent
dc.date2006-12-19
dc.date.accessioned2026-07-07T07:36:03Z
dc.date.available2026-07-07T07:36:03Z
dc.descriptionLet F be a non Archimedean locally compact field of residue characteristic different from 2, let G be a connected reductive group defined over F, let s be an involutive F-automorphism of G and H an open F-subgroup of the fixed points group of s. We denote by G(F) (resp. H(F)) the group of F-points of G (resp. H). In this paper, we obtain an analogue of the Cartan decomposition for the reductive symmetric space G(F)/H(F). More precisely, we obtain a decomposition of G(F) as a union of H(F)-cosets which is related to the H(F)-conjugacy classes of maximal s-anti-invariant F-split tori in G. When G is F-split, we get a more precise result, involving the stabilizer of a special point of the Bruhat-Tits building of G over F.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0612545
dc.identifierhttp://arxiv.org/abs/math/0612545
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120295
dc.subjectRepresentation Theory
dc.subjectGroup Theory
dc.subject22E50
dc.titleAn analogue of the Cartan decomposition for p-adic reductive symmetric spaces
dc.typetext

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