Representations of a reductive p-adic group in characteristic distinct from p

We investigate the irreducible cuspidal $C$-representations of a reductive $p$-adic group $G$ over field $C$ characteristic different from $p$. When is algebraically closed, for many groups $G$, list $C$-types $(J,\lambda)$ has been produced satisfying exhaustion, sometimes restricted kind representations, and often unicity. verify that those lists Aut($C$)-stability we produce similar when no longer assumed closed. Our other main results concern supercuspidality. This notion makes sense representations $\lambda$ in as above, which involve finite groups. check an representation induced supercuspidal if only supercuspidal.