Journal of Combinatorial Algebra


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Volume 1, Issue 1, 2017, pp. 1–44
DOI: 10.4171/JCA/1-1-1

Published online: 2016-12-13

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

Vaughan F. R. Jones[1]

(1) Vanderbilt University, Nashville, United States

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.

Keywords: Thompson group, subfactor, conformal field theory, diffeomorphism, planar algebra, partition function, knot, link, Seifert surface

Jones Vaughan: Some unitary representations of Thompson’s groups $F$ and $T$. J. Comb. Algebra 1 (2017), 1-44. doi: 10.4171/JCA/1-1-1