Bounded Cohomology and Unitary Representations of Automorphism Groups of Regular Trees

Abstract

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems to be the first instance where the continuous bounded cohomology is determined in all positive degrees with coefficients arising from any irreducible continuous unitary representations without being zero in all cases.