1. Groupes de Kac-Moody déployés n corps local II. Masures ordonnées
- Author
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Guy Rousseau, Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Kac-Moody group ,corps local ,corps valué ,General Mathematics ,010102 general mathematics ,local field ,enveloping algebra ,algèbre enveloppante ,MSC : 20G44 ,20G25 ,20E42 ,51E24 ,simple group ,16. Peace & justice ,01 natural sciences ,[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] ,groupe de Kac-Moody ,groupe simple ,immeuble ,building ,masure ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Mathematics::Representation Theory ,Mathematics - Group Theory ,Mathematics - Abstract
For a split Kac-Moody group (in J. Tits' definition) over a field endowed with a real valuation, we build an ordered affine hovel on which the group acts. This construction generalizes the one already done by S. Gaussent and the author when the residue field contains the complex field [Annales Fourier, 58 (2008), 2605-2657] and the one by F. Bruhat and J. Tits when the group is reductive. We prove that this hovel has all properties of ordered affine hovels (masures affines ordonn\'ees) as defined in [Rousseau, ArXiv 0810.4241]. We use the maximal Kac-Moody group as defined by O. Mathieu and we prove a few new results about it over any field; in particular we prove, in some cases, a simplicity result for this group., Comment: 61 pages
- Published
- 2016
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