On the Rankin–Selberg L-factors for SO5 × GL2

Abstract

Let π and τ be irreducible smooth generic representations of SO₅ and GL₂ respectively over a non-archimedean local field. We show that the L- and ε-factors attached to π×π defined by the Rankin–Selberg integrals and the associated Weil–Deligne representation coincide. The proof is obtained by explicating the relation between the Rankin–Selberg integrals for SO₅ × GL₂ and Novodvorsky’s local integrals for GSp₄× GL₂.