BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Fourier coefficients of theta functions on metaplectic groups Cai, Yuanqing


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.

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