Using the theta correspondence, we extend classification of irreducible representations quasi-split unitary groups (the so-called local Langlands which is due to Mok) non groups. We also prove that our satisfies some good properties, characterize it uniquely. In particular, this paper provides an alternative approach works Kaletha-Mínguez-Shin-White and Mœglin-Renard.

We show that local-global compatibility away from p holds at points on the (p-adic) eigenvariety of a definite unitary group which are étale over weight space. The novelty is we allow non-classical points. More precisely we interpolate the local Langlands correspondence across the eigenvariety by considering the stalks of its defining coherent sheaf. We employ techniques of Scholze from his rec...

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of [6, 4]. We prove this duality for the Kirillov–Reshetikhin modules. In the course of the proof we introduce and construct “interpolating (q, t)-characters” depending on two parameters which interpolate between the q-characte...