On discrete chamber-transitive automorphism groups of affine buildings

Abstract

Introduction. Let A be the affine building of a simple adjoint algebraic group Q of relative rank > 2 over a locally compact local field K. Let Aut A (resp. E Aut A) denote the group of type-preserving (resp. of all) automorphisms of A. Note that E Aut A contains the group $(K) of T-rational points of . We will be interested in discrete subgroups of Aut A which are chamber-transitive on A. It is extremely rare that such groups exist and, as can therefore be expected, exceptions are interesting phenomena; our purpose is to list them all (see the theorem below). In order to describe them we must first introduce some notation.