{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/97530"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/97530","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"Volume Formula and Intersection Pairings of N-fold Reduced Products","abstract":"Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an N-fold reduced product of G. In 2008, Suzuki and Takakura gave a volume formula of N-fold reduced products of SU(3) via Riemann-Roch. We compare our volume formula with theirs and prove that our volume formula matches theirs in the case of triple reduced products of SU(3).","abstract_html":"Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an N-fold reduced product of G. In 2008, Suzuki and Takakura gave a volume formula of N-fold reduced products of SU(3) via Riemann-Roch. We compare our volume formula with theirs and prove that our volume formula matches theirs in the case of triple reduced products of SU(3).","abstract_has_math":false,"creators":["Ji, Jia"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Mathematics","school":null,"contributors":[],"advisors":["Jeffrey, Lisa C"],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-11","date_published":"2019-11","updated_at":"2026-07-27T21:28:02Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/97530","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Jeffrey, Lisa C"]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Ji, Jia"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-11"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2019-11-14T00:00:42Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-11-14T00:00:42Z"]},{"key":"dc:date.issued","label":"Date","values":["2019-11"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/97530"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an N-fold reduced product of G. In 2008, Suzuki and Takakura gave a volume formula of N-fold reduced products of SU(3) via Riemann-Roch. We compare our volume formula with theirs and prove that our volume formula matches theirs in the case of triple reduced products of SU(3)."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Volume Formula and Intersection Pairings of N-fold Reduced Products"]}]}],"canonical_facts":{"dc:contributor.advisor":["Jeffrey, Lisa C"],"dc:contributor.department":["Mathematics"],"dc:creator":["Ji, Jia"],"dc:date":["2019-11"],"dc:date.accessioned":["2019-11-14T00:00:42Z"],"dc:date.available":["2019-11-14T00:00:42Z"],"dc:date.issued":["2019-11"],"dc:description.abstract":["Let G be a semisimple compact connected Lie group. An N-fold reduced product of G is the symplectic quotient of the Hamiltonian system of the Cartesian product of N coadjoint orbits of G under diagonal coadjoint action of G. Under appropriate assumptions, it is a symplectic orbifold. Using the technique of nonabelian localization and the residue formula of Jeffrey and Kirwan, we investigate the symplectic volume and the intersection pairings of an N-fold reduced product of G. In 2008, Suzuki and Takakura gave a volume formula of N-fold reduced products of SU(3) via Riemann-Roch. We compare our volume formula with theirs and prove that our volume formula matches theirs in the case of triple reduced products of SU(3)."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1807/97530"],"dc:title":["Volume Formula and Intersection Pairings of N-fold Reduced Products"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:28:02Z"}