The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\\lambda$, for each dominant integral form $\\lambda$ on the Lie algebra of a maximal torus of $G$.
","abstract_html":"<p>The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\\lambda$, for each dominant integral form $\\lambda$ on the Lie algebra of a maximal torus of $G$.</p>","abstract_has_math":true,"creators":["Timchenko, Kostiantyn"],"institution":null,"degree_name":"Master of Science in Mathematics (M.S.)","degree_level":"Thesis (open access)","degree_discipline":"Department of Mathematical Sciences","degree_department":null,"school":null,"contributors":["Francois Ziegler","Jimmy Dillies"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-01-01T08:00:00Z","date_published":"2014-01-01T08:00:00Z","updated_at":"2026-07-24T02:28:00Z","subjects":["ETD","Unitary representation","coadjoint orbit","geometric quantization","Kahler manifold","Geometry and Topology","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://digitalcommons.georgiasouthern.edu/etd/1144","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Francois Ziegler","Jimmy Dillies"]},{"key":"dc:creator","label":"Author","values":["Timchenko, Kostiantyn"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-07-07T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Department of Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis (open access)"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Mathematics (M.S.)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["ETD","Unitary representation","coadjoint orbit","geometric quantization","Kahler manifold","Geometry and Topology","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://digitalcommons.georgiasouthern.edu/etd/1144"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\\lambda$, for each dominant integral form $\\lambda$ on the Lie algebra of a maximal torus of $G$.
"]},{"key":"dc:title","label":"Title","values":["A Constructive Proof of the Borel-Weil Theorem for Classical Groups"]}]}],"canonical_facts":{"dc:contributor":["Francois Ziegler","Jimmy Dillies"],"dc:creator":["Timchenko, Kostiantyn"],"dc:date.available":["2014-07-07T07:00:00Z"],"dc:description.abstract":["The Borel-Weil theorem is usually understood as a realization theorem for representations that have already been shown to exist by other means (``Theorem of the Highest Weight''). In this thesis we turn the tables and show that, at least in the case of the classical groups $G = U(n)$, $SO(n)$ and $Sp(2n)$, the Borel-Weil construction can be used to quite explicitly prove existence of an irreducible representation having highest weight $\\lambda$, for each dominant integral form $\\lambda$ on the Lie algebra of a maximal torus of $G$.
"],"dc:identifier":["https://digitalcommons.georgiasouthern.edu/etd/1144"],"dc:subject":["ETD","Unitary representation","coadjoint orbit","geometric quantization","Kahler manifold","Geometry and Topology","Mathematics"],"dc:title":["A Constructive Proof of the Borel-Weil Theorem for Classical Groups"],"thesis:degree_discipline":["Department of Mathematical Sciences"],"thesis:degree_level":["Thesis (open access)"],"thesis:degree_name":["Master of Science in Mathematics (M.S.)"]},"updated_at":"2026-07-24T02:28:00Z"}