Analogs of principal series representations for Thompson's groups $F$ and $T$
Lukasz Garncarek
22D10Thompson's groupprincipal series representationinduced representation
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.
Indiana University Mathematics Journal
2012
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10.1512/iumj.2012.61.4572
10.1512/iumj.2012.61.4572
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Indiana Univ. Math. J. 61 (2012) 619 - 626
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