31 research outputs found
Parabolically induced unitary representations of the universal group U(F)^+ are C_0
By employing a new strategy we prove that all parabolically induced unitary
representations of the Burger-Mozes universal group U(F)^+, with F being
primitive, have all their matrix coefficients vanishing at infinity. This
generalizes the same well-known result for the universal group U(F)^+, when F
is 2-transitive.Comment: To appear in Math. Scan
The flat closing problem for buildings
Using the notion of a strongly regular hyperbolic automorphism of a locally
finite Euclidean building, we prove that any (not necessarily discrete) closed,
co-compact subgroup of the type-preserving automorphisms group of a locally
finite general non-spherical building contains a compact-by-Z^d subgroup, where
d is the dimension of a maximal flat.Comment: To appear in Algebraic and Geometric Topology, final versio
A unified proof of the Howe-Moore property
We provide a unified proof of all known examples of locally compact groups
that enjoy the Howe-Moore property, namely, the vanishing at infinity of all
matrix coefficients of the group unitary representations that are without
non-zero invariant vectors. These examples are: connected, non-compact, simple
real Lie groups with finite center, isotropic simple algebraic groups over non
Archimedean local fields and closed, topologically simple subgroups of Aut(T)
that act 2-transitively on the boundary at infinity of T, where T is a
bi-regular tree with valence > 2 at every vertex.Comment: Final version, to appear in Journal of Lie Theor