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arXiv · 2211.08555

Jones' representations of R. Thompson's groups not induced by finite-dimensional ones

Arnaud Brothier·Dilshan Wijesena
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Abstract

Given any linear isometry from a Hilbert space to its square one can explicitly construct a so-called Pythagorean unitary representation of Richard Thompson's group F. We introduce a condition on the isometry implying that the associated representation does not contain any induced representations by finite-dimensional ones. This provides the first result of this kind. We illustrate this theorem via a family of representations parametrised by the real 3-sphere for which all of them have this property except two sub-circles.

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Arnaud Brothier, Dilshan Wijesena. 2022-11-15. Jones' representations of R. Thompson's groups not induced by finite-dimensional ones. https://arxiv.org/abs/2211.08555

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