Year: 2026
Type: preprint
Abstract: Over any local field of characteristic zero, we develop a local theory of Jacquet-Shalika integrals that were originally introduced by Jacquet and Shalika to study exterior square local $L$-factors for $GL_m$. In particular, at least in the archimedean case, we establish a complete functional equation matching Artin local $\varepsilon$-factors. Central to the argument is a novel comparison strategy between Jacquet-Shalika integrals and open-orbit integrals associated to the Shalika subgroup.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7211865492