Celebratio Mathematica — Jones

On Jones’ connections between
subfactors, conformal field theory,
Thompson’s groups and knots

Works connected to Arnaud Brothier

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A. Brothier and V. F. R. Jones: “Pythagorean representations of Thompson’s groups,” J. Funct. Anal. 277 : 7 (October 2019), pp. 2442–2469. MR 3989149 Zbl 07089431 ArXiv 1807.06215 article

A. Brothier and V. F. R. Jones: “On the Haagerup and Kazhdan properties of R. Thompson’s groups,” J. Group Theory 22 : 5 (2019), pp. 795–807. MR 4000616 Zbl 07104291 ArXiv 1805.02177 article

A machinery developed by the second author produces a rich family of unitary representations of the Thompson groups \( F \), \( T \) and \( V \). We use it to give direct proofs of two previously known results. First, we exhibit a unitary representation of \( V \) that has an almost invariant vector but no nonzero \( [F,F] \)-invariant vectors reproving and extending Reznikoff’s result that any intermediate subgroup between the commutator subgroup of \( F \) and \( V \) does not have Kazhdan’s property (T) (though Reznikoff proved it for subgroups of \( T \)). Second, we construct a one parameter family interpolating between the trivial and the left regular representations of \( V \). We exhibit a net of coefficients for those representations which vanish at infinity on \( T \) and converge to 1 thus reproving that \( T \) has the Haagerup property after Farley who further proved that \( V \) has this property.

On Jones’ connections between subfactors, conformal field theory, Thompson’s groups and knots

Works connected to Arnaud Brothier

Filter the Bibliography List

On Jones’ connections between
subfactors, conformal field theory,
Thompson’s groups and knots