{"id":{"repo_id":"city-london","oai_identifier":"oai:openaccess.city.ac.uk:5915"},"canonical_url":"https://search.dev.ndltd.org/etd/city-london/oai:openaccess.city.ac.uk:5915","repository":{"repo_id":"city-london","name":"City University of London","base_url":"https://openaccess.city.ac.uk/cgi/oai2"},"display":{"title":"The representation theory of diagram algebras","abstract":"In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of the corresponding affine reflection group, we give a characterisation of the (limiting) blocks of the Brauer and partition algebras in positive characteristic. In the case of the Brauer algebra, we then show that simple reflections give rise to non-zero decomposition numbers. We then restrict our attention to a particular family of Brauer and partition algebras, and use the block result to determine the entire decomposition matrix of the algebras therein.","abstract_html":"In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of the corresponding affine reflection group, we give a characterisation of the (limiting) blocks of the Brauer and partition algebras in positive characteristic. In the case of the Brauer algebra, we then show that simple reflections give rise to non-zero decomposition numbers. We then restrict our attention to a particular family of Brauer and partition algebras, and use the block result to determine the entire decomposition matrix of the algebras therein.","abstract_has_math":false,"creators":["King, Oliver"],"institution":"City University London","degree_name":"phd","degree_level":"doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-09","date_published":"2014-09","updated_at":"2026-07-24T01:38:58Z","subjects":["QA Mathematics"],"languages":[],"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":["King, Oliver"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-09"]},{"key":"dc:date.issued","label":"Date","values":["2014-09"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Doctoral Theses","Department of Mathematics","School of Science & Technology Doctoral Theses","School of Mathematics, Computer Science & Engineering"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["City University London"]},{"key":"dc:relation.isreferencedby","label":"Dc Relation Isreferencedby","values":["https://openaccess.city.ac.uk/id/eprint/5915/"]},{"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":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["QA Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://openaccess.city.ac.uk/id/eprint/5915/1/King%2C_Oliver.pdf"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of the corresponding affine reflection group, we give a characterisation of the (limiting) blocks of the Brauer and partition algebras in positive characteristic. In the case of the Brauer algebra, we then show that simple reflections give rise to non-zero decomposition numbers. We then restrict our attention to a particular family of Brauer and partition algebras, and use the block result to determine the entire decomposition matrix of the algebras therein."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The representation theory of diagram algebras"]}]}],"canonical_facts":{"dc:creator":["King, Oliver"],"dc:date":["2014-09"],"dc:date.issued":["2014-09"],"dc:description.abstract":["In this thesis we study the modular representation theory of diagram algebras, in particular the Brauer and partition algebras, along with a brief consideration of the Temperley-Lieb algebra. The representation theory of these algebras in characteristic zero is well understood, and we show that it can be described through the action of a reflection group on the set of simple modules (a result previously known for the Temperley-Lieb and Brauer algebras). By considering the action of the corresponding affine reflection group, we give a characterisation of the (limiting) blocks of the Brauer and partition algebras in positive characteristic. In the case of the Brauer algebra, we then show that simple reflections give rise to non-zero decomposition numbers. We then restrict our attention to a particular family of Brauer and partition algebras, and use the block result to determine the entire decomposition matrix of the algebras therein."],"dc:format":["application/pdf"],"dc:identifier.uri":["https://openaccess.city.ac.uk/id/eprint/5915/1/King%2C_Oliver.pdf"],"dc:publisher.department":["Doctoral Theses","Department of Mathematics","School of Science & Technology Doctoral Theses","School of Mathematics, Computer Science & Engineering"],"dc:publisher.institution":["City University London"],"dc:relation.isreferencedby":["https://openaccess.city.ac.uk/id/eprint/5915/"],"dc:subject":["QA Mathematics"],"dc:title":["The representation theory of diagram algebras"],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T01:38:58Z"}