Abstract
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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