Nebbia's CCR conjecture for boundary-transitive groups on semi-regular trees
Let be a thick semi-regular tree, and let be a closed subgroup of acting transitively on the boundary . A locally compact group is CCR if is compact for every irreducible representation of and every . Nebbia's conjecture. Every such group is CCR.
The conjecture proposes that sufficiently regular boundary action forces regularity of the unitary dual. Earlier results establish implications from CCR or Type I assumptions to boundary transitivity, while the converse remains open in this generality.
References
Primary source
Lancelot Semal, “Irreducibly represented Lie groups and Nebbia's CCR conjecture on trees”, arXiv:2306.04310 (2023).
Additional references
2 papers in this index state this conjecture (2022–2023). The statement above is taken from the most recent of them; the others are arXiv:2203.04189.
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