{"id":{"repo_id":"ottawa-retro","oai_identifier":"oai:ruor.uottawa.ca:10393/49979"},"canonical_url":"https://search.dev.ndltd.org/etd/ottawa-retro/oai:ruor.uottawa.ca:10393/49979","repository":{"repo_id":"ottawa-retro","name":"University of Ottawa","base_url":"https://ruor.uottawa.ca/server/oai/request"},"display":{"title":"Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras","abstract":"In this thesis we construct a generalization of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a generalization of the divided difference and Demazure operators in the setting of the ring of Laurent polynomials 𝔏. We will construct a coinvariant algebra for the action of the hyperoctahedral group 𝑊_𝑛 on 𝔏. From these operators, we will be able to find a faithful representation of the Hecke algebra 𝓗_{𝑞,𝑝}(𝑊_𝑛) over 𝔏.","abstract_html":"In this thesis we construct a generalization of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a generalization of the divided difference and Demazure operators in the setting of the ring of Laurent polynomials 𝔏. We will construct a coinvariant algebra for the action of the hyperoctahedral group 𝑊_𝑛 on 𝔏. From these operators, we will be able to find a faithful representation of the Hecke algebra 𝓗_{𝑞,𝑝}(𝑊_𝑛) over 𝔏.","abstract_has_math":false,"creators":["Talarico, Marco"],"institution":"Université d'Ottawa / University of Ottawa","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Salmasian, Hadi"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-12-16T22:21:27Z","date_published":"2024-12-16T22:21:27Z","updated_at":"2026-07-24T03:39:16Z","subjects":["Representation Theory","Combinatorics","Hecke Algebras"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://doi.org/10.20381/ruor-30783"],"render_values":[{"text":"https://doi.org/10.20381/ruor-30783","href":"https://doi.org/10.20381/ruor-30783","code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10393/49979","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Salmasian, Hadi"]},{"key":"dc:creator","label":"Author","values":["Talarico, Marco"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2024-12-16T22:21:27Z","2024-12-16"]},{"key":"dc:publisher","label":"Institution","values":["Université d'Ottawa / University of Ottawa"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Representation Theory","Combinatorics","Hecke Algebras"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10393/49979","https://doi.org/10.20381/ruor-30783"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we construct a generalization of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a generalization of the divided difference and Demazure operators in the setting of the ring of Laurent polynomials 𝔏. We will construct a coinvariant algebra for the action of the hyperoctahedral group 𝑊_𝑛 on 𝔏. From these operators, we will be able to find a faithful representation of the Hecke algebra 𝓗_{𝑞,𝑝}(𝑊_𝑛) over 𝔏."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras"]}]}],"canonical_facts":{"dc:contributor":["Salmasian, Hadi"],"dc:creator":["Talarico, Marco"],"dc:date":["2024-12-16T22:21:27Z","2024-12-16"],"dc:description":["In this thesis we construct a generalization of the higher Specht polynomials to the Hecke algebra 𝓗_𝑞(𝑆_𝑛). These polynomials form a basis of the coinvariant algebra 𝕮 with respect to the action of 𝑆_𝑛, and they will decompose 𝕮 into irreducible representations of the Hecke algebra. These irreducible representations are 𝑞-Specht modules 𝑆_λ^𝑞. In this construction, if we consider 𝑞 = 1 then we obtain the original higher Specht polynomials for 𝑆_𝑛. We will also introduce a generalization of the divided difference and Demazure operators in the setting of the ring of Laurent polynomials 𝔏. We will construct a coinvariant algebra for the action of the hyperoctahedral group 𝑊_𝑛 on 𝔏. From these operators, we will be able to find a faithful representation of the Hecke algebra 𝓗_{𝑞,𝑝}(𝑊_𝑛) over 𝔏."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10393/49979","https://doi.org/10.20381/ruor-30783"],"dc:language":["en"],"dc:publisher":["Université d'Ottawa / University of Ottawa"],"dc:subject":["Representation Theory","Combinatorics","Hecke Algebras"],"dc:title":["Higher Specht Polynomials for Representations of Iwahori-Hecke Algebras"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T03:39:16Z"}