Godement--Jacquet L-function and homological theta lifting
Representation Theory
2025-07-11 v1 Number Theory
Abstract
In this paper we investigate the theta lifting of type II dual pairs over a non-Archimedean local field, by combining the homological method of Adams--Prasad--Savin and the analytic method of Fang--Sun--Xue. We have three main results: 1. we determine completely the big theta lift of an irreducible representation when its Godement--Jacquet L-function is holomorphic at a critical point; 2. we compute the big theta lift of all characters, hence determine the space of eigendistributions on matrix spaces for all characters; 3. we show that the Weil representation is projective if and only if the dual pair is almost in the stable range.
Cite
@article{arxiv.2507.07531,
title = {Godement--Jacquet L-function and homological theta lifting},
author = {Rui Chen and Yufeng Li and Xiaohuan Long and Chenhao Tang and Jialiang Zou},
journal= {arXiv preprint arXiv:2507.07531},
year = {2025}
}
Comments
42 pages, all comments are welcome!