Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/144251
Title: ENDOSCOPIC CHARACTER IDENTITIES FOR METAPLECTIC GROUPS
Authors: LUO CAIHUA
Keywords: local Langlands correspondence, endoscopy theory, metaplectic group, Howe finiteness conjecture, spherical fundamental lemma, R-group theory
Issue Date: 12-Jan-2018
Citation: LUO CAIHUA (2018-01-12). ENDOSCOPIC CHARACTER IDENTITIES FOR METAPLECTIC GROUPS. ScholarBank@NUS Repository.
Abstract: This thesis focuses on the so-called Langlands-Weissman program for covering groups, especially the project of the proof of endoscopic character identities for metaplectic groups in the spirit of J. Adams et al. Like the endoscopy theory for reductive groups, one is expected to, following J. Arthur's standard argument, produce the local Langlands correspondence and the global multiplicity formula for metaplactic groups. Based on the recent work of W. T. Gan and A. Ichino, what I have contributed is to prove the conjectural endoscopic character identities for metaplectic groups directly via a local-global argument instead of the standard argument. To do so, I have first proved the Howe finiteness conjecture for covering groups by adapting L. Clozel's argument for reductive groups, and then proved the spherical fundamental lemma for metaplectic groups following L. Clozel and T. Hales' method. Given those two necessary ingredients, this project follows from applying twice a simple stable trace formula. The last part of the thesis is devoted to convincing myself of the Knapp-Stein dimension theorem for covering groups which is a folklore without an explicit reference.
URI: http://scholarbank.nus.edu.sg/handle/10635/144251
Appears in Collections:Ph.D Theses (Open)

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