{"id":{"repo_id":"east-anglia","oai_identifier":"oai:ueaeprints.uea.ac.uk:48696"},"canonical_url":"https://search.dev.ndltd.org/etd/east-anglia/oai:ueaeprints.uea.ac.uk:48696","repository":{"repo_id":"east-anglia","name":"University of East Anglia","base_url":"https://ueaeprints.uea.ac.uk/cgi/oai2"},"display":{"title":"On the mod-p representations of unramified U(2,1)","abstract":"Let E=F be an unrami�ed quadratic extension of non-archimedean local �elds of odd residue characteristic p and let G be the unitary group in three variable U(2; 1)(E=F). In this thesis, we explore the smooth representation theory of G over a �eld ~E of characteristic p. The main results are as follows. Firstly, we have classi�ed the simple modules of the pro-p Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K0 of G and any irreducible smooth representation � of K0, and for any nonzero � 2 ~E , we have determined the subquotients of indG K0�=(T�","abstract_html":"Let E=F be an unrami�ed quadratic extension of non-archimedean local �elds of odd residue characteristic p and let G be the unitary group in three variable U(2; 1)(E=F). In this thesis, we explore the smooth representation theory of G over a �eld ~E of characteristic p. The main results are as follows. Firstly, we have classi�ed the simple modules of the pro-p Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K0 of G and any irreducible smooth representation � of K0, and for any nonzero � 2 ~E , we have determined the subquotients of indG K0�=(T�","abstract_has_math":false,"creators":["Xu, Peng"],"institution":"University of East Anglia","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-02","date_published":"2014-02","updated_at":"2026-07-24T02:12:01Z","subjects":[],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":null,"outbound_label":null,"outbound_source":null},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Xu, Peng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-02"]},{"key":"dc:date.issued","label":"Date","values":["2014-02"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["School of Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of East Anglia"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://ueaeprints.uea.ac.uk/id/eprint/48696/"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://ueaeprints.uea.ac.uk/id/eprint/48696/1/Thesis-Peng_Xu.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let E=F be an unrami�ed quadratic extension of non-archimedean local �elds of odd residue characteristic p and let G be the unitary group in three variable U(2; 1)(E=F). In this thesis, we explore the smooth representation theory of G over a �eld ~E of characteristic p. The main results are as follows. Firstly, we have classi�ed the simple modules of the pro-p Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K0 of G and any irreducible smooth representation � of K0, and for any nonzero � 2 ~E , we have determined the subquotients of indG K0�=(T�"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On the mod-p representations of unramified U(2,1)"]}]}],"canonical_facts":{"dc:creator":["Xu, Peng"],"dc:date":["2014-02"],"dc:date.issued":["2014-02"],"dc:description.abstract":["Let E=F be an unrami�ed quadratic extension of non-archimedean local �elds of odd residue characteristic p and let G be the unitary group in three variable U(2; 1)(E=F). In this thesis, we explore the smooth representation theory of G over a �eld ~E of characteristic p. The main results are as follows. Firstly, we have classi�ed the simple modules of the pro-p Iwahori-Hecke algebra of G and described the so-called supersingular ones, which is one-dimensional character. Secondly, for the hyperspecial maximal compact open subgroup K0 of G and any irreducible smooth representation � of K0, and for any nonzero � 2 ~E , we have determined the subquotients of indG K0�=(T�"],"dc:format":["application/pdf"],"dc:identifier.uri":["https://ueaeprints.uea.ac.uk/id/eprint/48696/1/Thesis-Peng_Xu.pdf"],"dc:language":["en"],"dc:publisher.department":["School of Mathematics"],"dc:publisher.institution":["University of East Anglia"],"dc:relation.isreferencedby":["https://ueaeprints.uea.ac.uk/id/eprint/48696/"],"dc:title":["On the mod-p representations of unramified U(2,1)"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T02:12:01Z"}