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arXiv · 2607.04908

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

Ravi Raghunathan
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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].

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BibTeXRIS

Ravi Raghunathan. 2026-07-06. On the exterior square $\varepsilon$-factors of $GL_n$. https://arxiv.org/abs/2607.04908

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