Epipelagic -packets and rectifying characters

• 成果类型: Article
• 署名作者: Kaletha, Tasho
• 署名单位: Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0566-4
• 发表日期: 2015
• 页码: 1-89
• 关键词: local langlands correspondence; supercuspidal l-packets; fundamental lemma; trace formula; REPRESENTATIONS; isocrystals; PROOF

摘要

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 -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 , 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.