Reducibility points and characteristic p local fields I Simple supercuspidal representations of symplectic groups.

Let F be a non-Archimedean local field with odd characteristic p. Let N be a positive integer and G=Sp_2N(F). By work of Lomelí on γ-factors of pairs and converse theorems, a generic supercuspidal representation π of G has a transfer to a smooth irreducible representation Π_π of GL_2N+1(F). In turn the Weil–Deligne representation Σ_π associated to Π_π by the Langlands correspondence determines a Langlands parameter ϕ_π for π. This process produces a Langlands correspondence for generic cuspidal representations of G. In this paper we take π to be simple in the sense of Gross and Reeder, and from the explicit construction of π we describe Π_π explicitly. The method we use is the same as
in a previous paper, where we treated the case where F is a p-adic field. It relies on a criterion due to Mœglin on the reducibility of representations parabolically induced from GL_M(F)xG for varying positive integers M. We extend this criterion to the case when F has any positive characteristic. The main new feature consists in relating reducibility to γ-factors for pairs.