{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/30146"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/30146","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Representations of Cherednik algebras in positive characteristic","abstract":"In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the \"quantum\" case, where \"Planck's constant\" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the \"classical\" case, where \"Planck's constant\" is zero and generic irreducible representations have dimension r. Secondly, we classify the irreducible representations of the trigonometric Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. In one case, the \"Planck's constant\" is zero, and generic irreducible representations have dimension 2; one-dimensional irreducible representations exist when the \"coupling constant\" is also zero. In the other case, the \"Planck's constant\" is nonzero, and generic irreducible representations have dimension 2p; if the \"coupling constant\" is an even integer 0 =/< k =/< p - 1, then there exist smaller irreducible representations of dimensions p + k and p - k.","abstract_html":"In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the "quantum" case, where "Planck's constant" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the "classical" case, where "Planck's constant" is zero and generic irreducible representations have dimension r. Secondly, we classify the irreducible representations of the trigonometric Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. In one case, the "Planck's constant" is zero, and generic irreducible representations have dimension 2; one-dimensional irreducible representations exist when the "coupling constant" is also zero. In the other case, the "Planck's constant" is nonzero, and generic irreducible representations have dimension 2p; if the "coupling constant" is an even integer 0 =/< k =/< p - 1, then there exist smaller irreducible representations of dimensions p + k and p - k.","abstract_has_math":false,"creators":["Latour, Frédéric"],"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":2004,"date_issued":"2004","date_published":"2004","updated_at":"2026-07-22T22:22:30Z","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/1721.1/30146","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. 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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/1721.1/30146"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.","Includes bibliographical references (p. 67-68)."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the \"quantum\" case, where \"Planck's constant\" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the \"classical\" case, where \"Planck's constant\" is zero and generic irreducible representations have dimension r. Secondly, we classify the irreducible representations of the trigonometric Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. In one case, the \"Planck's constant\" is zero, and generic irreducible representations have dimension 2; one-dimensional irreducible representations exist when the \"coupling constant\" is also zero. In the other case, the \"Planck's constant\" is nonzero, and generic irreducible representations have dimension 2p; if the \"coupling constant\" is an even integer 0 =/< k =/< p - 1, then there exist smaller irreducible representations of dimensions p + k and p - k."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Representations of Cherednik algebras in positive characteristic"]}]}],"canonical_facts":{"dc:contributor.advisor":["Pavel Etingof."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Latour, Frédéric"],"dc:date.accessioned":["2006-03-24T18:23:50Z"],"dc:date.available":["2006-03-24T18:23:50Z"],"dc:date.issued":["2004"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.","Includes bibliographical references (p. 67-68)."],"dc:description.abstract":["In this thesis, we first classify the irreducible representations of the rational Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. One is the \"quantum\" case, where \"Planck's constant\" is nonzero and generic irreducible representations have dimension pr, where r is the order of the cyclic group contained in the algebra. The other is the \"classical\" case, where \"Planck's constant\" is zero and generic irreducible representations have dimension r. Secondly, we classify the irreducible representations of the trigonometric Cherednik algebras of rank 1 in characteristic p > 0. There are two cases. In one case, the \"Planck's constant\" is zero, and generic irreducible representations have dimension 2; one-dimensional irreducible representations exist when the \"coupling constant\" is also zero. In the other case, the \"Planck's constant\" is nonzero, and generic irreducible representations have dimension 2p; if the \"coupling constant\" is an even integer 0 =/< k =/< p - 1, then there exist smaller irreducible representations of dimensions p + k and p - k."],"dc:description.degree":["Ph.D."],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/1721.1/30146"],"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":["Representations of Cherednik algebras in positive characteristic"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:22:30Z"}