Epipelagic $$L$$L-packets and rectifying characters

By Tasho Kaletha. 2012

63 citations recorded by the source corpus.

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 $$L$$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 $$\mathrm{{GL}}_n$$GLn, 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8e10898aa5eec8fb8f2e4ff1977da58723ef3b4

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In Geometry and Topology

1. Tasho Kaletha
2. Mark Reeder
3. J. Yu
4. Jessica Fintzen
5. W. Gan
6. B. Gross
7. Zhiwei Yun

In Mathematical Physics

1. Tasho Kaletha
2. Mark Reeder
3. J. Yu
4. Jessica Fintzen
5. W. Gan
6. B. Gross
7. Zhiwei Yun

Citations in the corpus

• Genericity and contragredience in the local Langlands correspondence (2012, methodology): “For general connected reductive groups, there are constructions of the correspondence for specific classes of parameters, including the classical case of unramified representations, the case of representations with Iwahori-fixed vector by work of Kazhdan–Lusztig, unipotent representations by work of”
• Rigid inner forms of real and p-adic groups (2013, result): “ral diagram similar to (1.2). It was shown by the author [Kal14] that the work [DR09] ofDeBackerandReederextends tothis setting andthatthe endoscopic characteridentitieshold. Furthermore,thesameistrue[KalEpi]foradifferentclassof supercuspidal Langlands parameters, for which the corresponding L-packe”
• Epipelagic representations and invariant theory (2013, methodology): “This was carried out by Kaletha [18] in work based on an earlier version of this paper.”