English

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 FF and TT, which are analogs of principal series representations of SL(2,R)SL(2,\R). 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 FF and TT 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