Germ expansion, endoscopic transfer, and unitary periods

In this thesis, we study the germ expansions in the Jacquet-Rallis transfer. We prove an identity that relates certain nilpotent orbital integrals for any smooth matching in this transfer. We give two applications of this identity. For the first, we give an elementary local proof of the endoscopic fundamental lemma for unitary groups (theorem of Laumon and Ngo). For the second, we establish a new relative trace formula comparison conjectured by Jacquet that can be used to study unitary periods.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2019

Author dc:creator

• Xiao, Jingwei,Ph.D.Massachusetts Institute of Technology.

Advisor dc:contributor.advisor

• Wei Zhang.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/122178

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/122178