On the Local Langlands Functoriality Transfer From SO(5) to GL(4)

We study the local Langlands functoriality transfer from SO(5, F) to GL(4, F) for arbitrary twists of several families of irreducible supercuspidal representations of GL(4, F), where F is a non-archimedean local field of characteristic zero. In doing so, we give equivalent conditions for such representations to be functoriality transfers from SO(5, F) in terms of the Bushnell-Kutzko construction of supercuspidal representations by studying poles of local exterior square L-functions and the existence of non-zero local Shalika models. This article provides a starting point for an explicit characterization of this functoriality transfer in terms of type theory.