Galois-fixed points in the Bruhat-Tits building of a reductive group
We give a new proof of a useful result of Guy Rousseau on Galois-fixed points in the Bruhat-Tits building of a reductive group.
We give a new proof of a useful result of Guy Rousseau on Galois-fixed points in the Bruhat-Tits building of a reductive group.
Let be a disjoint iteration group on the unit circle , that is a family of homeomorphisms such that for , and each either is the identity mapping or has no fixed point ( is a -divisible nontrivial Abelian group). Denote by the set of all cluster points of , for . In this paper we give a general construction of disjoint iteration groups for which .
Let G be a group of automorphisms of a tree X (with set of vertices S) and H a kernel on S × S invariant under the action of G. We want to give an estimate of the -operator norm (1 ≤ r ≤ 2) of the operator associated to H in terms of a norm for H. This was obtained by U. Haagerup when G is the free group acting simply transitively on a homogeneous tree. Our result is valid when X is a locally finite tree and one of the orbits of G is the set of vertices at even distance from a given vertex; a technical...