{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/64606"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/64606","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Unitary representations of rational Cherednik algebras and Hecke algebras","abstract":"We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2].","abstract_html":"We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2].","abstract_has_math":false,"creators":["Stoica, Emanuel (Emanuel I.)"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Pavel Etingof."],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:21:35Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/64606","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Pavel Etingof."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/64606"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 49-50)."]},{"key":"dc:description.abstract","label":"Abstract","values":["We begin the study of unitary representations in the lowest weight category of rational Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection groups and provide a complete classification in the case of the symmetric group. We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2]."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Unitary representations of rational Cherednik algebras and Hecke algebras"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pavel Etingof."],"dc:contributor.department":["Massachusetts Institute of Technology. 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We conclude that the KZ functor defined in [16] preserves unitarity in type A. Finally, we formulate a few conjectures concerning the classification of unitary representations for other types and the preservation of unitarity by the KZ functor and the restriction functors defined in [2]."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/64606"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Unitary representations of rational Cherednik algebras and Hecke algebras"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:35Z"}