Local theta correspondences between epipelagic supercuspidal\n representations

2015/01/28 by Hung Yean Loke, Jia-Jun Ma, Loke, Hung Yean +4
Mathematics · #22E46 #22E47 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1501.07069

openalex publication_date 2015/01/28 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this paper we study the local theta correspondences between epipelagic\nsupercupsidal representations of a type I classical dual pair (G,G') over\np-adic fields. We show that, besides an exceptional case, an epipelagic\nsupercupsidal representation \π of widetildeG lifts to an epipelagic\nsupercupsidal representation \π' of widetildeG' if and only if the\nepipelagic data of \π and \π' are related by the moment maps.\n

Citations

• A proof of the Howe duality conjecture

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• On input and Langlands parameters for epipelagic representations
• Theta correspondence for symplectic-orthogonal and metaplectic-orthogonal p-adic dual pairs
• Base change and theta correspondences for supercuspidal representations\n of SL(2)