Let F be a non-archimedean local field, and G be split orthogonal groups of odd degrees $\geq$ 3.

In this setting, my question is;
Is there explicit descriptions of maximal compact subgroups of G?

I am especially interested in the case that the residue field of F has characteristic 2.

Any reference or comments, or answers for this question or for general cases (e.g. classical p-adic groups) would be appreciated.

  • 1
    $\begingroup$ As with any reductive $p$-adic group, these are the stabilisers of points in the extended building. What counts as an explicit answer? If you're interested, Tits's Corvallis article discusses the quasi-split but non-split case. $\endgroup$
    – LSpice
    Mar 21, 2021 at 3:36
  • 1
    $\begingroup$ Did you check : Schémas en groupes et immeubles des groupes classiques sur un corps local. II : groupes unitaires, Bruhat, F. ; Tits, J., Bulletin de la Société Mathématique de France, Tome 115 (1987) , pp. 141-195 ? They give models for the buildings of classical groups in any characteristic. $\endgroup$ Apr 28, 2021 at 18:10
  • $\begingroup$ Thank you all. I try them. $\endgroup$
    – Aut
    May 4, 2021 at 8:34


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