Gaëtan Chenevier, Wee Teck Gan
Published 2023-03-28Version 1
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.
Geometric realization of the local Langlands correspondence for representations of conductor three
Reductions of semi-stable representations using the Iwahori mod $p$ Local Langlands Correspondence
Change of coefficients in the $p \neq \ell$ local Langlands correspondence for $GL_n$
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