Refined anisotropic K-types and supercuspidal representations

Abstract

Let F be a nonarchimedean local field, and G a connected reductive group defined over F . We classify the representations of G(F ) that contain any anisotropic unrefined minimal K-type satisfying a certain tameness condition. We show that these representations are induced from compact (mod center) subgroups, and we construct corresponding refined minimal K-types.