Analogs of principal series representations for Thompson's groups $F$ and $T$
Representation Theory
2013-04-15 v2 Group Theory
Abstract
We define series of representations of the Thompson's groups and , which are analogs of principal series representations of . We show that they are irreducible and classify them up to unitary equivalence. We also prove that they are different from representations induced from finite-dimensional representations of stabilizers of points under natural actions of and on the unit interval and the unit circle, respectively.
Keywords
Cite
@article{arxiv.1008.1275,
title = {Analogs of principal series representations for Thompson's groups $F$ and $T$},
author = {Łukasz Garncarek},
journal= {arXiv preprint arXiv:1008.1275},
year = {2013}
}
Comments
(v1) 5 pages; (v2) 7 pages; a substantially rewritten version; improved presentation; some new material on induced representations; removed the "Another approach..." section