We construct a family of unitary representations of the group . We show that this family of representations exhibits a “phase transition” analogous to that observed by Bost and Connes  and then explain how these representations are related to the equilibrium states of Bost and Connes.
Cite this article
Tyrone Crisp, The Bost–Connes phase transition and unitary representations. J. Noncommut. Geom. 7 (2013), no. 1, pp. 291–300DOI 10.4171/JNCG/117