On Jones' subgroup of R. Thompson's group T

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Jordan Nikkel, Yunxiang Ren

Published: 01 Jan 2018, Last Modified: 06 Oct 2025Int. J. Algebra Comput. 2018EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Jones introduced unitary representations for the Thompson groups F and T from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups F→ and T→. Golan and Sapir studied F→ and identified it as a copy of the Thompson group F3. In this paper, we completely describe T→ and show that T→ coincides with its commensurator in T, implying that the corresponding unitary representation is irreducible. We also generalize the notion of the Stallings 2-core for diagram groups to T, showing that T→ and T3 are not isomorphic, but as annular diagram groups they have very similar presentations.