The irreducible orthogonal and symplectic Galois representations of a p-adic field (the tame case)

Abstract

Let F be a p-adic field. If n is a natural number relatively prime to p, then all the irreducible n-dimensional Galois representations are parametrized by admissible characters. This parametrization is used to determine which of these characters are real-valued, and among the real-valued representations to distinguish the orthogonal representations from the symplectic representations.