${\rm Spin}(7)$ is unacceptable

Gaëtan Chenevier; Wee Teck Gan

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arXiv · 2303.15897

${\rm Spin}(7)$ is unacceptable

Gaëtan Chenevier·Wee Teck Gan

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Abstract

We classify the pairs of group morphisms $\Gamma \rightarrow {\rm Spin}(7)$ which are element conjugate but not globally conjugate. As an application, we study the case where $\Gamma$ is the Weil group of a $p$-adic local field, which is relevant to the recent approach to the local Langlands correspondence for ${\rm G}_2$ and ${\rm PGSp}_6$ by Gan and Savin. As a second application, we improve some result of Kret and Shin about ${\rm GSpin}_7$-valued Galois representations.

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Gaëtan Chenevier, Wee Teck Gan. 2023-03-28. ${\rm Spin}(7)$ is unacceptable. https://arxiv.org/abs/2303.15897

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