A Godement-Jacquet type integral and the metaplectic Shalika model
Number Theory
2020-05-14 v1 Representation Theory
Abstract
We present a novel integral representation for a quotient of global automorphic L-functions, the symmetric square over the exterior square. The pole of this integral characterizes a period of a residual representation of an Eisenstein series. As such, the integral itself constitutes a period, of an arithmetic nature. The construction involves the study of local and global aspects of a new model for double covers of general linear groups, the metaplectic Shalika model. In particular, we prove uniqueness results over p-adic and Archimedean fields, and a new Casselman-Shalika type formula.
Keywords
Cite
@article{arxiv.1603.01671,
title = {A Godement-Jacquet type integral and the metaplectic Shalika model},
author = {Eyal Kaplan and Jan Möllers},
journal= {arXiv preprint arXiv:1603.01671},
year = {2020}
}