{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T04:31:59Z","timestamp":1764131519284},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,8]]},"abstract":"<jats:p> Jones introduced unitary representations for the Thompson groups [Formula: see text] and [Formula: see text] from a given subfactor planar algebra. Some interesting subgroups arise as the stabilizer of certain vector, in particular the Jones subgroups [Formula: see text] and [Formula: see text]. Golan and Sapir studied [Formula: see text] and identified it as a copy of the Thompson group [Formula: see text]. In this paper, we completely describe [Formula: see text] and show that [Formula: see text] coincides with its commensurator in [Formula: see text], implying that the corresponding unitary representation is irreducible. We also generalize the notion of the Stallings 2-core for diagram groups to [Formula: see text], showing that [Formula: see text] and [Formula: see text] are not isomorphic, but as annular diagram groups they have very similar presentations. <\/jats:p>","DOI":"10.1142\/s0218196718500388","type":"journal-article","created":{"date-parts":[[2018,5,18]],"date-time":"2018-05-18T11:05:17Z","timestamp":1526641517000},"page":"877-903","source":"Crossref","is-referenced-by-count":3,"title":["On Jones\u2019 subgroup of R. Thompson\u2019s group T"],"prefix":"10.1142","volume":"28","author":[{"given":"Jordan","family":"Nikkel","sequence":"first","affiliation":[{"name":"Vanderbilt University, Nashville, United States"}]},{"given":"Yunxiang","family":"Ren","sequence":"additional","affiliation":[{"name":"The University of Tennessee, Knoxville, United States"}]}],"member":"219","published-online":{"date-parts":[[2018,8,17]]},"reference":[{"key":"S0218196718500388BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(87)90015-6"},{"issue":"3","key":"S0218196718500388BIB002","first-page":"215","volume":"42","author":"Cannon J. W.","year":"1996","journal-title":"Enseign. Math. (2)"},{"key":"S0218196718500388BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2016.09.001"},{"key":"S0218196718500388BIB004","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/6982"},{"issue":"620","key":"S0218196718500388BIB006","first-page":"viii+117","volume":"130","author":"Guba V.","year":"1997","journal-title":"Mem. Amer. Math. Soc."},{"key":"S0218196718500388BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389127"},{"key":"S0218196718500388BIB008","doi-asserted-by":"publisher","DOI":"10.4171\/JCA\/1-1-1"},{"key":"S0218196718500388BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-017-2945-3"},{"key":"S0218196718500388BIB011","series-title":"Chicago Lectures in Mathematics","volume-title":"The Theory of Unitary Group Representations","author":"Mackey G. W.","year":"1976"},{"key":"S0218196718500388BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/BF02095993"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500388","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:17:33Z","timestamp":1565097453000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,8]]},"references-count":10,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2018,8,17]]},"published-print":{"date-parts":[[2018,8]]}},"alternative-id":["10.1142\/S0218196718500388"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500388","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,8]]}}}