We show that a mod-ℓ-representation of p-adic group arising from the analogue Yu's construction is supercuspidal if and only it arises representation finite reductive group. This has been previously shown by Henniart Vigneras under assumption second adjointness holds.

Let K/F be a quadratic extension of p-adic fields. We show that a generic irreducible representation of GL(n, K) is distinguished if and ony if its Rankin-Selberg Asai L-function has an exceptional pole at zero. We use this result to compute Asai L-functions of ordinary irreducible representations of GL(2, K). In the appendix, we describe supercuspidal dihedral representations of GL(2, K) in te...

Let G be any connected reductive group defined over a nonarchimedean local field F of residual characteristic p. Under some tameness assumptions on G, we construct families of positive-depth supercuspidal representations of G = G(F ). In particular, we classify (§2.7) the representations of G that contain any anisotropic unrefined minimal K-type (in the sense of MoyPrasad [28]) that satisfies a...

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu’s construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu’s construction, Fourier transforms of orbital integr...