Descent and theta functions for covering groups

Solomon Friedberg

This lecture concerns the use of automorphic descent methods (which in turn are based on unipotent orbits) for covering groups. More specifically, we study descent integrals for covering groups and use them to construct square-integrable representations by descending theta functions. This leads us to conjecture relations between theta representations on different covering groups. In particular, this suggests that the conjecture of Patterson (1983) for the theta function on the four-fold cover of $GL_2$ is the first in a series of relations. This work is joint with David Ginzburg.

http://scgp.stonybrook.edu/video_portal/video.php?id=2843

Simons- Program: Automorphic forms, mock modular forms and string theory