A construction of the Deligne-Langlands local root numbers of orthogonal Galois representations (Q910430)

Let K be a local p-adic field and v a continuous orthogonal Galois representation factoring through \(Gal(K/{\mathbb{Q}}_ p)\). The author gives a representation-theoretic description of the local root number \(W_ K(v)\) using the Atiyah-Segal completion theorem in orthogonal K-theory and explicit Brauer induction.