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 text pdf 10.1512/iumj.2012.61.4572 10.1512/iumj.2012.61.4572 en Indiana Univ. Math. J. 61 (2012) 619 - 626 state-of-the-art mathematics http://iumj.org/access/