{"id":{"repo_id":"penn","oai_identifier":"oai:repository.upenn.edu:20.500.14332/28824"},"canonical_url":"https://search.dev.ndltd.org/etd/penn/oai:repository.upenn.edu:20.500.14332/28824","repository":{"repo_id":"penn","name":"University of Pennsylvania","base_url":"https://repository.upenn.edu/server/oai/request"},"display":{"title":"On Decomposition of the Product of Demazure atoms and Demazure Characters","abstract":"This thesis studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes.","abstract_html":"This thesis studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes.","abstract_has_math":false,"creators":["Pun, Ying Anna"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["James Haglund"],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01","date_published":"2016-01-01","updated_at":"2026-07-24T03:45:26Z","subjects":[],"languages":["en"],"rights":["Ying Anna Pun"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://repository.upenn.edu/handle/20.500.14332/28824","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["James Haglund"]},{"key":"dc:creator","label":"Author","values":["Pun, Ying Anna"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-05-17T16:06:18.000"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-05-22T16:52:02Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-04-27T00:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2016-01-01"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation/Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Ying Anna Pun"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://repository.upenn.edu/handle/20.500.14332/28824"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Doctor of Philosophy (PhD)"]},{"key":"dc:format.mimetype","label":"Dc Format Mimetype","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["On Decomposition of the Product of Demazure atoms and Demazure Characters"]}]}],"canonical_facts":{"dc:contributor.advisor":["James Haglund"],"dc:creator":["Pun, Ying Anna"],"dc:date":["2023-05-17T16:06:18.000"],"dc:date.accessioned":["2023-05-22T16:52:02Z"],"dc:date.available":["2016-04-27T00:00:00Z"],"dc:date.issued":["2016-01-01"],"dc:description.abstract":["This thesis studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes."],"dc:description.degree":["Doctor of Philosophy (PhD)"],"dc:format.mimetype":["application/pdf"],"dc:identifier.uri":["https://repository.upenn.edu/handle/20.500.14332/28824"],"dc:language":["en"],"dc:rights":["Ying Anna Pun"],"dc:title":["On Decomposition of the Product of Demazure atoms and Demazure Characters"],"dc:type":["Dissertation/Thesis"]},"updated_at":"2026-07-24T03:45:26Z"}