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RADU GROUPS ACTING ON TREES ARE CCR
Part of
LANCELOT SEMAL
Journal:

Journal of the Australian Mathematical Society / Volume 117 / Issue 2 / October 2024

Published online by Cambridge University Press:

06 March 2024, pp. 149-186

Print publication:

October 2024
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We classify the irreducible unitary representations of closed simple groups of automorphisms of trees acting $2$-transitively on the boundary and whose local action at every vertex contains the alternating group. As an application, we confirm Claudio Nebbia’s CCR conjecture on trees for $(d_0,d_1)$-semi-regular trees such that $d_0,d_1\in \Theta $, where $\Theta $ is an asymptotically dense set of positive integers.