Local theta correspondences between epipelagic supercuspidal representations

Abstract

In this paper we study the local theta correspondences between epipelagic supercupsidal representations of a type I classical dual pair $(G,G^{\prime })$ over $p$-adic fields. We show that, besides an exceptional case, an epipelagic supercupsidal representation $\pi$ of $\tilde{G}$ lifts to an epipelagic supercupsidal representation ${\pi }^{\prime }$ of ${\tilde{G}}^{\prime }$ if and only if the epipelagic data of $\pi$ and ${\pi }^{\prime }$ are related by the moment maps.

References in corpus (1)

• A proof of the Howe duality conjecture