Non-unitarisable representations and random forests
Group Theory
2010-01-20 v2 Functional Analysis
Abstract
We establish a connection between Dixmier's unitarisability problem and the expected degree of random forests on a group. As a consequence, a residually finite group is non-unitarisable if its first L2-Betti number is non-zero or if it is finitely generated with non-trivial cost. Our criterion also applies to torsion groups constructed by D. Osin, thus providing the first examples of non-unitarisable groups not containing a non-Abelian free subgroup.
Cite
@article{arxiv.0811.3422,
title = {Non-unitarisable representations and random forests},
author = {Inessa Epstein and Nicolas Monod},
journal= {arXiv preprint arXiv:0811.3422},
year = {2010}
}