Geometric Waldspurger periods II
Representation Theory
2023-08-25 v4
Abstract
In this paper we extend the calculation of the geometric Waldspurger periods from our paper math/0510110 to the case of ramified coverings. We give some applications to the study of Whittaker coefficients of the theta-lifting of automorphic sheaves from PGL_2 to the metaplectic group Mp_2, they agree with our conjectures from arXiv:1211.1596. In the process of the proof, we get some new automorphic sheaves for GL_2 in the ramified setting. We also formulate stronger conjectures about Waldspurger periods and geometric theta-lifting for the dual pair (SL_2, Mp_2).
Keywords
Cite
@article{arxiv.1308.6531,
title = {Geometric Waldspurger periods II},
author = {Sergey Lysenko},
journal= {arXiv preprint arXiv:1308.6531},
year = {2023}
}
Comments
59 pages, final version, to appear in Representation theory (electronic J. of AMS)