A construction of the deligne–langlands local root numbers of orthogonal galois representations

Abstract

I will give a new description of the Deligne-Langlands local root numbers, WK(v), when v is an orthogonal Galois representation. Firstly, let us briefly recapitulate the theory of these local root numbers (sometimes called local constants). Let K be a non-Archimedean local field. For simplicity, we will assume that char(K) =O. Let R, denote the absolute Galois group of K and suppose that r:Q,-+U,(C) is a continuous, unitary Galois representation. To such a 1’ is associated the Deligne-Langlands root number [3,5,1 I] Ii&(V)ESi. (2)