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Some unitary representations of Thompson’s groups $$F$$ and $$T$$. (English) Zbl 06684911
Summary: 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.

##### MSC:
 20F38 Other groups related to topology or analysis 46L37 Subfactors and their classification 57M25 Knots and links in the $$3$$-sphere (MSC2010) 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
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