{"pk":64829,"title":"The Hurwitz action in complex reflection groups","subtitle":null,"abstract":"We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive and give a simple criterion to tell when two shortest reflection factorizations belong to the same Hurwitz orbit. We also characterize the quasi-Coxeter elements (those with a shortest reflection factorization that generates the whole group) in $G(m, p, n)$.\n \nMathematics Subject Classifications: 05A05, 05A15, 05E18, 20F55","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Hurwitz action"},{"word":"reflection factorization"},{"word":"complex reflection group"},{"word":"dual Coxeter theory"},{"word":"braid action and quasi-Coxeter element"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/4xg2m191","frozenauthors":[{"first_name":"Joel","middle_name":"Brewster","last_name":"Lewis","name_suffix":"","institution":"Department of Mathematics, George Washington University, Washington, D.C., U.S.A.","department":""},{"first_name":"Jiayuan","middle_name":"","last_name":"Wang","name_suffix":"","institution":"Department of Mathematics, George Washington University, Washington, D.C., U.S.A.","department":""}],"date_submitted":"2022-03-23T20:30:28Z","date_accepted":"2022-03-23T20:30:28Z","date_published":"2022-03-31T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64829/galley/49639/download/"}]}