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 $T$,\nwhich are analogs of principal series representations of $SL(2,\\R)$. We show\nthat they are irreducible and classify them up to unitary equivalence. We also\nprove that they are different from representations induced from\nfinite-dimensional representations of stabilizers of points under natural\nactions of $F$ and $T$ on the unit interval and the unit circle, respectively.\n