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

Abstract

We define series of representations of the Thompson's groups $F$ and $T$, which are analogs of principal series representations of $SL(2,\mathbb{R})$. 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.

(v1) 5 pages; (v2) 7 pages; a substantially rewritten version; improved presentation; some new material on induced representations; removed the "Another approach..." section

Cited by in corpus (4)

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• Jones representations of Thompson's group $F$ arising from Temperley-Lieb-Jones algebras
• On the oriented Thompson subgroup ${\vec{F}}_3$ and its relatives in higher Brown-Thompson groups
• Irreducible Pythagorean representations of R. Thompson's groups and of the Cuntz algebra