Functions conditionally of negative type on groups acting on regular trees

Abstract

Let ${\mathcal{T}}_{q+1}$ be the $(q+1)$-regular tree and let $G$ be a group of automorphisms acting transitively on the vertices and on the boundary of ${\mathcal{T}}_{q+1}$. We give an upper bound for the growth of cocycles with values in any unitary representation of the group $G$. This bound is optimal by projecting the Haagerup cocycle onto an appropriate subspace of ${\ell }^2(E)$. We also obtain a description of functions conditionally of negative type which are unbounded.

Cited by in corpus (3)

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