{"paper":{"title":"On Jones Subgroup of R. Thompson's Group $T$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Jordan Nikkel, Yunxiang Ren","submitted_at":"2017-10-19T00:33:49Z","abstract_excerpt":"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 $\\vec{F}$ and $\\vec{T}$. Golan and Sapir studied $\\vec{F}$ and identified it as a copy of the Thompson group $F_3$. In this paper we completely describe $\\vec{T}$ and show that $\\vec{T}$ 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 $T$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06972","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}