Restricting cuspidal representations of the group of automorphisms of a homogeneous tree
Donald I. Cartwright, Gabriella Kuhn (2003)
Bollettino dell'Unione Matematica Italiana
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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...