A note on type I groups acting on d-regular trees
Group Theory
2015-06-10 v1 Functional Analysis
Representation Theory
Abstract
In this note, we give new examples of type I groups generalizing a previous result of Ol'shanskii. More precisely, we prove that all closed non-compact subgroups of Aut(T_d) acting transitively on the vertices and on the boundary of a d-regular tree and satisfying Tits' independence property are type I groups. We claim no originality as we use standard ingredients: the polar decomposition of those groups and the admissibility of all their irreducible unitary representations.
Cite
@article{arxiv.1506.02950,
title = {A note on type I groups acting on d-regular trees},
author = {Corina Ciobotaru},
journal= {arXiv preprint arXiv:1506.02950},
year = {2015}
}