Let G be Sp(2n, F) (resp. SO(2n + 1, F)), where F is a p-adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation of G an m-tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of . We show that this correspondence respects the induction and Jacquet module fu...

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 ...

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.

• Higher commutators • Godement’s principle: bounding dimensions of irreducibles • The von Neumann (strong) density theorem • Lie’s Theorem on irreducible finite-dimensional representations of connected solvable groups • Separating families of irreducible finite-dimensional representations • Subrepresentation Theorem for finite-dimensional representations of reductive linear real Lie groups • T...

In this paper, we survey some mathematical developments that followed from the discovery of simple supercuspidal representations p-adic groups.