{"id":{"repo_id":"anu","oai_identifier":"oai:openresearch-repository.anu.edu.au:1885/133596"},"canonical_url":"https://search.dev.ndltd.org/etd/anu/oai:openresearch-repository.anu.edu.au:1885/133596","repository":{"repo_id":"anu","name":"Australian National University","base_url":"https://openresearch-repository.anu.edu.au/server/oai/request"},"display":{"title":"A graphical calculus for shifted symmetric functions","abstract":"The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and Olshanski [OO97]. This isomorphism lends us a graphical description of some important bases of the algebra of shifted symmetric functions. Conversely, we are also able to describe some important generators of the centre of the Heisenberg category in the language of shifted symmetric functions. This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00].","abstract_html":"The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and Olshanski [OO97]. This isomorphism lends us a graphical description of some important bases of the algebra of shifted symmetric functions. Conversely, we are also able to describe some important generators of the centre of the Heisenberg category in the language of shifted symmetric functions. This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00].","abstract_has_math":false,"creators":["Mitchell, Stuart Arpad"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T00:54:41Z","subjects":["Representation theory","symmetric groups","free probability","Heisenberg category","categorification"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b47393051"],"render_values":[{"text":"b47393051","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/1885/133596","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Mitchell, Stuart Arpad"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-11-13T01:44:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-11-13T01:44:30Z"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:type","label":"Dc Type","values":["Thesis (MPhil)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Representation theory","symmetric groups","free probability","Heisenberg category","categorification"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["b47393051"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1885/133596"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and Olshanski [OO97]. This isomorphism lends us a graphical description of some important bases of the algebra of shifted symmetric functions. Conversely, we are also able to describe some important generators of the centre of the Heisenberg category in the language of shifted symmetric functions. This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00]."]},{"key":"dc:title","label":"Title","values":["A graphical calculus for shifted symmetric functions"]}]}],"canonical_facts":{"dc:creator":["Mitchell, Stuart Arpad"],"dc:date.accessioned":["2017-11-13T01:44:30Z"],"dc:date.available":["2017-11-13T01:44:30Z"],"dc:date.issued":["2017"],"dc:description.abstract":["The goal of this thesis is twofold. The fi rst goal is to describe three categori cations of the algebra of symmetric functions and establish relationships between them all. The second goal is to establish an isomorphism between the centre of Khovanov's Heisenberg category [Kho14] and the algebra of shifted symmetric functions defined by Okounkov and Olshanski [OO97]. This isomorphism lends us a graphical description of some important bases of the algebra of shifted symmetric functions. Conversely, we are also able to describe some important generators of the centre of the Heisenberg category in the language of shifted symmetric functions. This turns out to be given in the language of free probability, in particular, the transition and co-transition measures of Kerov [Ker93, Ker00]."],"dc:identifier.other":["b47393051"],"dc:identifier.uri":["http://hdl.handle.net/1885/133596"],"dc:language.iso":["en"],"dc:subject":["Representation theory","symmetric groups","free probability","Heisenberg category","categorification"],"dc:title":["A graphical calculus for shifted symmetric functions"],"dc:type":["Thesis (MPhil)"]},"updated_at":"2026-07-24T00:54:41Z"}