{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/108489"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/108489","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Wreath Macdonald polynomials as eigenstates","abstract":"We show that the wreath Macdonald polynomials for $\\ZZ/\\ell\\ZZ\\wr\\Sigma_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\\qqq,\\ddd}(\\ddot{\\mathfrak{sl}}_\\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods.","abstract_html":"We show that the wreath Macdonald polynomials for <span class=\"etd-inline-math\">\\ZZ/\\ell\\ZZ\\wr\\Sigma<sub>n</sub></span>, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra <span class=\"etd-inline-math\">U<sub>\\qqq,\\ddd</sub>(\\ddot{\\mathfrak{sl}}<sub>\\</sub>ell)</span>, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods.","abstract_has_math":true,"creators":["Wen, Joshua Jeishing"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dodd, Christopher","Kedem, Rinat","di Francesco, Philippe","Katz, Sheldon"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-10-07T20:59:51Z","date_published":"2020-10-07T20:59:51Z","updated_at":"2026-07-22T22:24:48Z","subjects":["Macdonald polynomials","quantum toroidal algebras"],"languages":["en"],"rights":["Copyright 2020 Joshua Wen"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/108489","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dodd, Christopher","Kedem, Rinat","di Francesco, Philippe","Katz, Sheldon"]},{"key":"dc:creator","label":"Author","values":["Wen, Joshua Jeishing"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-10-07T20:59:51Z","2020-07-16","2020-08"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Macdonald polynomials","quantum toroidal algebras"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Joshua Wen"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/108489"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We show that the wreath Macdonald polynomials for $\\ZZ/\\ell\\ZZ\\wr\\Sigma_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\\qqq,\\ddd}(\\ddot{\\mathfrak{sl}}_\\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Joshua Wen, accepted the attached license on 2020-07-14 at 13:25.","The student, Joshua Wen, submitted this Dissertation for approval on 2020-07-14 at 13:29.","This Dissertation was approved for publication on 2020-07-16 at 15:33.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15608 on 2020-10-02 at 15:13:23","Made available in DSpace on 2020-10-07T20:59:51Z (GMT). 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Our proof makes heavy use of shuffle algebra methods.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-10-02 without embargo terms","The student, Joshua Wen, accepted the attached license on 2020-07-14 at 13:25.","The student, Joshua Wen, submitted this Dissertation for approval on 2020-07-14 at 13:29.","This Dissertation was approved for publication on 2020-07-16 at 15:33.","DSpace SAF Submission Ingestion Package generated from Vireo submission #15608 on 2020-10-02 at 15:13:23","Made available in DSpace on 2020-10-07T20:59:51Z (GMT). No. of bitstreams: 2 WEN-DISSERTATION-2020.pdf: 588045 bytes, checksum: 573aae6094903cd7c38ef3f7fe2ee709 (MD5) LICENSE.txt: 4207 bytes, checksum: 0435b2885ffb9acd03888ac66039f5d8 (MD5) Previous issue date: 2020-07-16"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/108489"],"dc:language":["en"],"dc:rights":["Copyright 2020 Joshua Wen"],"dc:subject":["Macdonald polynomials","quantum toroidal algebras"],"dc:title":["Wreath Macdonald polynomials as eigenstates"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:48Z"}