Représentations intégrables du groupe de De Sitter
This paper is concerned with the action of a special formally real Jordan algebra U on an Euclidean space E, with the decomposition of E under this action and with an application of this decomposition to the study of Bessel functions on the self-adjoint homogeneous cone associated to U.
Let be a homogeneous tree in which every vertex lies on edges, where . Let be the group of automorphisms of , and let be the its subgroup , where is a local field whose residual field has order . We consider the restriction to of a continuous irreducible unitary representation of . When is spherical or special, it was well known that remains irreducible, but we show that when is cuspidal, the situation is much more complicated. We then study in detail what happens when the...