Langlands parameters for epipelagic representations of GLn\text{\rm GL}_n

Let $F$ be a non-Archimedean local field. An irreducible cuspidal representation of $\text{\rm GL}_n(F)$ is epipelagic if its Swan conductor equals 1. We give a full and explicit description of the Langlands parameters of such representations.Comment: 25 page

Tame multiplicity and conductor for local Galois representations

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$. Let $\sigma$ be an irreducible smooth representation of the absolute Weil group \Cal W_F of $F$ and \sw(\sigma) the Swan exponent of $\sigma$. Assume \sw(\sigma) \ge1. Let \Cal I_F be the inertia subgroup of \Cal W_F and \Cal P_F the wild inertia subgroup. There is an essentially unique, finite, cyclic group $\varSigma$, of order prime to $p$, so that \sigma(\Cal I_F) = \sigma(\Cal P_F)\varSigma. In response to a query of Mark Reeder, we show that the multiplicity in $\sigma$ of any character of $\varSigma$ is bounded by \sw(\sigma).Comment: Revised version with further detai

Types et contragr\'edientes

Let G be a p-adic reductive group, and R an algebraically closed field. Let us consider a smooth representation of G on an R-vector space V. Fix an open compact subgroup K of G and a smooth irreducible representation of K on a finite-dimensional R-vector space W. The space of K-homomorphisms from W to V is a right module over the intertwining algebra H(G,K,W). We examine how those constructions behave when we pass to the contragredient representations of V and W, and we give conditions under which the behaviour is the same as in the case of complex representations. We take an abstract viewpoint and use only general properties of G. In the last section, we apply this to the theory of types for the group GL(n) and its inner forms over a non-Archimedean local field.Comment: 15 pages, in Frenc