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.

中文翻译：

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RADU 团体对树木采取行动是 CCR

我们对树的自同构封闭简单群的不可约酉表示进行分类 $2$ -在边界上传递，并且其在每个顶点的局部动作都包含交替群。作为一个应用，我们证实了 Claudio Nebbia 对树的 CCR 猜想 $(d_0,d_1)$ - 半规则树，这样 $d_0,d_1\in \Theta $ ， 在哪里 $\西塔$ 是正整数的渐近稠密集。