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 of $\overrightarrow F < F$ and $\overrightarrow T < T$ which allow us to produce all oriented knots and links.

汤普森群的一些酉表示 $F类$ 和 $T型$

沃恩·F·R·琼斯

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