The Local Langlands Conjecture for

A paper of Reeder–Yu [J. Amer. Math. Soc. 27 (2014), pp. 437–477] gives a construction of epipelagic supercuspidal representations of p p -adic groups. The input for this construction is a pair ( λ , χ ) (\lambda , \chi ) where λ \lambda is a stable vector in a certain representation coming from a Moy–Prasad filtration, and χ \chi is a character of the additive group of the residue field. We say two such pairs are equivalent if the resulting supercuspidal representations are isomorphic. In this paper we describe the equivalence classes of such pairs. As an application, we give a classification of the simple supercuspidal representations for split adjoint groups. Finally, under an assumption about unramified base change, we describe properties of the Langlands parameters associated to these simple supercuspidals, showing that they have trivial L-functions and minimal Swan conductors, and showing that each of these simple supercuspidals lies in a singleton L-packet.

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The Local Langlands Conjecture for

Abstract: We prove the local Langlands conjecture for the exceptional group $G_2(F)$ where F is a non-archimedean local field of characteristic zero.

Cited by 3 publications

References 47 publications

Computation of Fourier coefficients of automorphic forms of type $$G_2$$

Computation of Fourier coefficients of automorphic forms of type $$G_2$$

$$\textrm{Spin}(7)$$ Is Unacceptable

On input and Langlands parameters for epipelagic representations

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