Factorization of the local exterior square L-function of GL_m

Let π be an irreducible generic representation of GL_m(F) , where F is a non-Archimedean local field. In 1990, Jacquet and Shalika established an integral representation of exterior square L-functions of GL_m(F). Following the works of Cogdell and Piatetski-Shapiro, we characterize exceptional poles in terms of certain Shalika functionals on the derivatives of π, where “derivatives” are in the sense of Bernstein and Zelevinsky. We prove the factorization of local L-functions, which was originally observed by Cogdell and Piatetski-Shapiro: local exterior square L-functions can be expressed in terms of exceptional L-functions of the derivatives of π.