Godement–Jacquet L-function and homological theta lifting
Published:
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.
Links: arXiv:2507.07531