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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

The Explicit Local Langlands Correspondence for G2

Résumé

We develop a general strategy for constructing explicit Local Langlands correspondences for p-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an example of our general strategy, we construct explicit Local Langlands Correspondence for the exceptional group G2 over an arbitrary non-archimedean local field, with explicit L-packets and explicit matching between the group side and the Galois side. For intermediate series, we use our previous result on Hecke algebras by the first and third authors. For principal series, we improve on previous works of Muic etc.~and obtain more explicit descriptions on both group and Galois sides. Moreover, we show the existence of non-unipotent singular supercuspidal representations of G2, and exhibit them in \textit{mixed} L-packets mixing supercuspidals with non-supercuspidals. Furthermore, our LLC satisfies a list of expected properties, including the AMS Conjecture on cuspidal support.

Dates et versions

hal-03830529 , version 1 (26-10-2022)

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Anne-Marie Aubert, Yujie Xu. The Explicit Local Langlands Correspondence for G2. 2022. ⟨hal-03830529⟩
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