Transformation Groups

, Volume 7, Issue 1, pp 15-50

Building ofGL(m, D) and centralizers

  • P. BroussousAffiliated withDépartement de Mathématiques, Université de Poitiers
  • , B. LemaireAffiliated withCNRS (UMR 8628), Université de Paris-Sud

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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.I E) the nonextended affine building ofG (resp. of the centralizer ofE x inG). In this paper we prove that there exists a uniqueG E-equivariant affine mapj E∶IE→I. It is injective and its image coincides with the set ofE x-fixed points inI. Moreover, we prove thatj E is compatible with the Moy-Prasad filtrations.