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Epipelagic \(L\)-packets and rectifying characters

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Abstract

We provide an explicit construction of the local Langlands correspondence for general tamely-ramified reductive p-adic groups and a class of wildly ramified Langlands parameters. Furthermore, we verify that our construction satisfies many expected properties of such a correspondence. More precisely, we show that each \(L\)-packet we construct admits a parameterization in terms of the Langlands dual group, contains a unique generic element for a fixed Whittaker datum, satisfies the formal degree conjecture, is compatible with central and cocentral characters, provides a stable virtual character, and satisfies the expected endoscopic character identities. Moreover, we show that in the case of \(\mathrm{{GL}}_n\), our construction coincides with the established local Langlands correspondence. Our techniques provide a general approach to the construction of the local Langlands correspondence for tamely-ramified groups and regular supercuspidal parameters.

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Notes

  1. I thank Loren Spice for alerting me about this reduction argument.

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Acknowledgments

This work has profited greatly from enlightening and inspiring mathematical conversations with Stephen DeBacker, Benedict Gross, Guy Henniart, Atsushi Ichino, Robert Kottwitz, Mark Reeder, and Loren Spice. It is a pleasure to thank these mathematicians for their interest and support.

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  1. Department of Mathematics, Princeton University Fine Hall, Washington Road, Princeton, NJ, 08540, USA

    Tasho Kaletha

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Correspondence to Tasho Kaletha.

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This research is supported in part by NSF Grant DMS-1161489.

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Kaletha, T. Epipelagic \(L\)-packets and rectifying characters. Invent. math. 202, 1–89 (2015). https://doi.org/10.1007/s00222-014-0566-4

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