Let $F$ be a non-archimedean local field of residual characteristic $p \neq 2$ . $G$ (connected) reductive group over that splits tamely ramified extension We revisit Yu's construction smooth complex representations $G(F)$ from slightly different perspective and provide proof the resulting are supercuspidal. also counterexample to Proposition 14.1 Theorem 14.2 in Yu [ Construction tame supercus...

We generalize the methods of Moy-Prasad, in order to define and study the genuine depth zero representations of some nonlinear covers of reductive groups over p-adic local fields. In particular, we construct all depth zero supercuspidal representations of the metaplectic group Mp2n over a p-adic field of odd residue characteristic.

In this paper we prove a conjecture of Jacquet about supercuspidal representations of GLn(K ) distinguished by GLn(k), or by Un(k), for K a quadratic unramified extension of a non-Archimedean local field k.

The author's work with Murnaghan on distinguished tame supercuspidal representations is re-examined using a simplified treatment of Jiu-Kang Yu's construction $p$-adic reductive groups. This leads to unification aspects the theories cuspidal over and finite fields.