Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions

The global twisted GGP conjecture is a variant of the Gan-Gross-Prasad conjecture for unitary groups, and considers the restriction of an automorphic representation of GL(V ) to its subgroup U(V ), for a skew-Hermitian space V. It relates the nonvanishing of a certain period integral to the central value of an L-function attached to the representation. In this thesis, using a relative trace formula approach, we prove the global twisted GGP conjecture in the unramified case, under some additional local assumptions on the quadratic extension and the automorphic representation. In particular, we reduce the required fundamental lemma to the Jacquet-Rallis fundamental lemma.

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

2024

Author dc:creator

• Wang, Danielle

Advisor dc:contributor.advisor

• Zhang, Wei

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/155315

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/155315