Open Collections

Fourier coefficients of theta functions on metaplectic groups

Banff International Research Station for Mathematical Innovation and Discovery

Kazhdan and Patterson constructed generalized theta functions on covers of general linear groups as multi-residues of the Borel Eisenstein series. These representations and their unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for $\text{GL}(r)$. In this talk, we will discuss the two other types of models that the theta representations may support. We first talk about semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondly, we determine the unipotent orbits attached to theta functions, in the sense of Ginzburg. We also determine the covers when these models are unique. Time permitting, we will discuss some applications in Rankin-Selberg constructions.

Mathematics; Number theory; Quantum theory

video/mp4

Author affiliation: Boston College

2017-02-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/60408

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/