Decomposition of Pythagorean representations of R. Thompson's groups

2023/02/09 by Brothier, Arnaud, Wijesena, Dilshan
#FOS: Mathematics #Group Theory (math.GR) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2302.04458

Abstract

We continue to study Pythagorean unitary representation of Richard Thompson's groups F, T and V that are built from a single isometry from a Hilbert space to its double. By developing powerful diagrammatically based techniques we show that each such representation splits into a diffuse and an atomic parts. We previously proved that the diffuse part is Ind-mixing: it does not contain induced representations of finite-dimensional ones. We fully decompose the atomic part: the building blocks are monomial representations arising from a precise family of parabolic subgroups of F.

Related

• Atomic representations of R. Thompson's groups and Cuntz's algebra
• Jones' representations of R. Thompson's groups not induced by finite-dimensional ones
• Pythagorean representations of Thompson's groups
• A tensor product for representations of the Cuntz algebra and of the R. Thompson groups
• Irreducibility of the Wysiwyg representations of Thompson's groups