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RADU GROUPS ACTING ON TREES ARE CCR

Part of: Locally compact groups and their algebras Structure and classification of infinite or finite groups Low-dimensional topology

Published online by Cambridge University Press:  06 March 2024

LANCELOT SEMAL
LANCELOT SEMAL*
Affiliation:
UCLouvain, 1348 Louvain-la-Neuve, Belgium
*
e-mail: [email protected]
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Abstract

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.

Keywords

unitary representationsgroups of automorphisms of semi-regular treestype I groupsNebbia’s conjecture

MSC classification

Primary: 22D12: Other representations of locally compact groups
Secondary: 20E08: Groups acting on trees 57M07: Topological methods in group theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 117 , Issue 2 , October 2024 , pp. 149 - 186
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by George Willis

The author is an F.R.S.-FNRS Research Fellow.

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