{"id":{"repo_id":"umn","oai_identifier":"oai:conservancy.umn.edu:11299/190477"},"canonical_url":"https://search.dev.ndltd.org/etd/umn/oai:conservancy.umn.edu:11299/190477","repository":{"repo_id":"umn","name":"University of Minnesota","base_url":"https://conservancy.umn.edu/server/oai/request"},"display":{"title":"A Local Trace Formula and the Multiplicity One Theorem for the Ginzburg-Rallis Model","abstract":"Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for all tempered L-packets. In some cases, we also proved the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. Finally, in the archimedean case, we proved some partial results for the general generic representations by applying the open orbit method.","abstract_html":"Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for all tempered L-packets. In some cases, we also proved the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. Finally, in the archimedean case, we proved some partial results for the general generic representations by applying the open orbit method.","abstract_has_math":false,"creators":["Wan, Chen"],"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":"2017-05","date_published":"2017-05","updated_at":"2026-07-24T05:20:03Z","subjects":["Harmonic Analysis on Spherical Varieties","Local Trace Formula","Multiplicity One on Vogan Packet"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11299/190477","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Wan, Chen"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2017-10-09T16:52:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2017-10-09T16:52:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2017-05"]},{"key":"dc:type","label":"Dc Type","values":["Thesis or Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Harmonic Analysis on Spherical Varieties","Local Trace Formula","Multiplicity One on Vogan Packet"]}]},{"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.uri","label":"Identifier URI","values":["http://hdl.handle.net/11299/190477"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["University of Minnesota Ph.D. dissertation.May 2017. Major: Mathematics. Advisor: Dihua Jiang. 1 computer file (PDF); iv, 213 pages."]},{"key":"dc:description.abstract","label":"Abstract","values":["Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for all tempered L-packets. In some cases, we also proved the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. Finally, in the archimedean case, we proved some partial results for the general generic representations by applying the open orbit method."]},{"key":"dc:title","label":"Title","values":["A Local Trace Formula and the Multiplicity One Theorem for the Ginzburg-Rallis Model"]}]}],"canonical_facts":{"dc:creator":["Wan, Chen"],"dc:date.accessioned":["2017-10-09T16:52:11Z"],"dc:date.available":["2017-10-09T16:52:11Z"],"dc:date.issued":["2017-05"],"dc:description":["University of Minnesota Ph.D. dissertation.May 2017. Major: Mathematics. Advisor: Dihua Jiang. 1 computer file (PDF); iv, 213 pages."],"dc:description.abstract":["Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove a local trace formula for the Ginzburg-Rallis model. Then by applying that trace formula, we prove a multiplicity formula for the Ginzburg-Rallis model for tempered representations. Using that multiplicity formula, we prove the multiplicity one theorem for all tempered L-packets. In some cases, we also proved the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. Finally, in the archimedean case, we proved some partial results for the general generic representations by applying the open orbit method."],"dc:identifier.uri":["http://hdl.handle.net/11299/190477"],"dc:language.iso":["en"],"dc:subject":["Harmonic Analysis on Spherical Varieties","Local Trace Formula","Multiplicity One on Vogan Packet"],"dc:title":["A Local Trace Formula and the Multiplicity One Theorem for the Ginzburg-Rallis Model"],"dc:type":["Thesis or Dissertation"]},"updated_at":"2026-07-24T05:20:03Z"}