Transformation Groups

, Volume 7, Issue 1, pp 15–50

Building ofGL(m, D) and centralizers

  • P. Broussous
  • B. Lemaire

DOI: 10.1007/BF01253463

Cite this article as:
Broussous, P. & Lemaire, B. Transformation Groups (2002) 7: 15. doi:10.1007/BF01253463


LetG=GL(m, D) whereD is a central division algebra over a commutative nonarchimedean local fieldF. LetE/F be a field extension contained inM(m, D). We denote byI (resp.IE) the nonextended affine building ofG (resp. of the centralizer ofEx inG). In this paper we prove that there exists a uniqueGE-equivariant affine mapjE∶IE→I. It is injective and its image coincides with the set ofEx-fixed points inI. Moreover, we prove thatjE is compatible with the Moy-Prasad filtrations.

Copyright information

© Birkhäuser 2002

Authors and Affiliations

  • P. Broussous
    • 1
  • B. Lemaire
    • 2
  1. 1.Département de MathématiquesUniversité de PoitiersFuturoscope Chasseuneuil CedexFrance
  2. 2.CNRS (UMR 8628)Université de Paris-SudOrsay CedexFrance