Analogs of principal series representations for Thompson's groups $F$ and $T$

Details Analogs of principal series representations for Thompson's groups $F$ and $T$ Analogs of principal series representations for Thompson's groups $F$ and $T$

2010-08-06

arxiv.org/abs/1008.1275v2

Mathematics

Representation Theory

(v1) 5 pages; (v2) 7 pages; a substantially rewritten version; improved presentation; some new material on induced representat

Scientific paper

We define series of representations of the Thompson's groups $F$ and $T$, which are analogs of principal series representations of $SL(2,\R)$. 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 $F$ and $T$ on the unit interval and the unit circle, respectively.

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