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

2022/11/15 by Arnaud Brothier, Brothier, Arnaud, Dilshan Wijesena +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematics and Applications #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2211.08555

openalex publication_date 2022/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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