I was wondering could anyone tell me a reference for the fact that an absolutely quasi-simple algebraic group over a non-archimedean local field which is centreless and non-compact acts faithfully and Weyl transitively on a regular locally finite building, and its image in the automorphism group is closed in the compact-open topology?
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$\begingroup$ That the image in the automorphism group is closed is a consequence of the properness of the action, which itself follows since the building is locally finite and the vertex stabilizers are compact. $\endgroup$– YCorCommented Oct 2, 2014 at 18:59
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For such a general assertion, independent of classification, you'd need some one of the F. Bruhat and J. Tits papers, but (since I do not have copies nearby) I could not point you to any precise location within them.
F. Bruhat and J. Tits, BN-paires de type affine et donnees radicielles, C.R. Acad. Sci. Paris serie A, vol 263 (1966), pp. 598-601.
F. Bruhat and J. Tits, Groupes simples residuellement deployes sur un corps local, ibid, pp. 766-768.
F. Bruhat and J. Tits, Groupes algebriques simples sur un corps local, ibid, pp. 822-825.
F. Bruhat and J. Tits, Groupes algebriques simple sur un corps local: cohomologie galoisienne, decomposition d'Iwasawa et de Cartan, ibid, pp. 867-869.
F. Bruhat and J. Tits, Groupes Reductifs sur un Corps Local, I: Donnees radicielles valuees, Publ. Math. I.H.E.S. 41 (1972), pp. 5-252.
F. Bruhat and J. Tits, Groupes Reductifs sur un Corps Local, II: Schemas en groups, existence d'une donnee radicielle valuee, ibid 60 (1984), pp. 5-184.
F. Bruhat and J. Tits, Schemas en groupes et immeubles des groupes classiques sur un corps local, Bull. Soc. Math. Fr. 112 (1984), pp. 259-301.
F. Bruhat and J. Tits, Groupes Reductifs sur un Corps Local, III: Complements et applications a la cohomologie galoisienne, J. Fac. Sci. Univ. Tokyo 34 (1987), pp. 671-688.
answered Oct 2, 2014 at 14:06