{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,21]],"date-time":"2025-05-21T08:49:58Z","timestamp":1747817398049,"version":"3.40.4"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"NSF","award":["DMS 2202017"],"award-info":[{"award-number":["DMS 2202017"]}]},{"name":"DFG","award":["SCHW 1550\/4-1"],"award-info":[{"award-number":["SCHW 1550\/4-1"]}]},{"name":"ARC","award":["DP180102437"],"award-info":[{"award-number":["DP180102437"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:p> We develop precise geometric descriptions of the conjugacy class [Formula: see text] and coconjugation set [Formula: see text] for all elements [Formula: see text] of any affine Coxeter group [Formula: see text]. The centralizer of x in [Formula: see text] is the special case [Formula: see text]. The key structure in our description of the conjugacy class [Formula: see text] is the mod-set [Formula: see text], where w is the finite part of x and [Formula: see text] is the coroot lattice. The set [Formula: see text] is then described by [Formula: see text] together with the fix-set of [Formula: see text], where [Formula: see text] is the finite part of [Formula: see text]. For any element w of the associated finite Weyl group W, the mod-set of w is contained in the classical move-set [Formula: see text]. We prove that the rank of [Formula: see text] equals the dimension of [Formula: see text] and investigate type-by-type the surprisingly subtle structure of [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196725500109","type":"journal-article","created":{"date-parts":[[2025,2,4]],"date-time":"2025-02-04T07:55:11Z","timestamp":1738655711000},"page":"403-465","source":"Crossref","is-referenced-by-count":1,"title":["The geometry of conjugation in affine Coxeter groups"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5212-1707","authenticated-orcid":false,"given":"Elizabeth","family":"Mili\u0107evi\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics & Statistics, Haverford College, 370 Lancaster Avenue, Haverford, PA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3377-6051","authenticated-orcid":false,"given":"Petra","family":"Schwer","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Heidelberg University, Im Neuenheimer Feld 255, 69120 Heidelberg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9074-4553","authenticated-orcid":false,"given":"Anne","family":"Thomas","sequence":"additional","affiliation":[{"name":"Anne Thomas, School of Mathematics & Statistics, Carslaw Building F07, University of Sydney NSW 2006, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,3,21]]},"reference":[{"key":"S0218196725500109BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-89394-3"},{"key":"S0218196725500109BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196715400135"},{"key":"S0218196725500109BIB003","first-page":"1","volume":"25","author":"Carter R. 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