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The Local Langlands Conjecture for G₂

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arxiv 2209.07346 v2 pith:F4ZPMFCG submitted 2022-09-15 math.NT

The Local Langlands Conjecture for G₂

Wee Teck Gan , Gordan Savin This is my paper
classification math.NT
keywords localconjecturelanglandscharacteristicexceptionalfieldgroupnon-archimedean
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We prove the local Langlands conjecture for the exceptional group $G_2(F)$ where $F$ is a non-archimedean local field of characteristic zero.

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  1. Non-admissibility of some universal supersingular representations

    math.NT 2026-05 unverdicted novelty 5.0

    For n greater than or equal to 3 and sufficiently generic weights, the universal supersingular representation of GL_n(k) is non-admissible and of infinite length.