Building ofGL(m, D) and centralizers
- 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.