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

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Vaughan Jones, Vanderbilt
Fine Hall 314

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