# Some unitary representations of Thompson's groups F and T

December 24, 2014

In a "naive" attempt to create algebraic quantum field theories on the
circle, we obtain a family of unitary representations of Thompson's groups T
and F for any subfactor. The Thompson group elements are the "local scale
transformations" of the theory. In a simple case the coefficients of the
representations are polynomial invariants of links. We show that all links
arise and introduce new "oriented" subgroups $\overrightarrow F <F$ and
$\overrightarrow T< T$ which allow us to produce all \emph{oriented} knots and
links.

Keywords:

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