On the exterior square $\varepsilon$-factors of $GL_n$

Ravi Raghunathan

On the exterior square $\varepsilon$-factors of $GL_n$

Number Theory 2026-07-06 v1

Authors: Ravi Raghunathan

Abstract

Let $\pi$ be a generic representation of ${\mathrm{GL}}_r(F)$ , where $F$ is a $p$ -adic field. We show using global methods that the $\varepsilon$ -factors associated to the exterior square of $\pi$ via the Jacquet-Shalika integrals and Langlands-Shahidi methods coincide. Along the way we also give a new proof of the local functional equation in the $p$ -adic case following the techniques in [Beuzart-Plessis, Relative trace formulas, Simons Symp.(2021), pages 1-50].

Keywords

epsilon-factors exterior square generic representation p-adic field Jacquet-Shalika integrals Langlands-Shahidi method

Cite

@article{arxiv.2607.04908,
  title  = {On the exterior square $\varepsilon$-factors of $GL_n$},
  author = {Ravi Raghunathan},
  journal= {arXiv preprint arXiv:2607.04908},
  year   = {2026}
}

Comments

19 pages