Local Langlands correspondence, local factors, and zeta integrals in analytic families
Local Langlands correspondence, local factors, and zeta integrals in analytic families
We study the variation of the local Langlands correspondence for GLn in characteristic-zero families.We establish an existence and uniqueness theorem for a correspondence in families, as well as a recognition theorem for when a given pair of Galois-and reductive-group-representations can be identified as local Langlands correspondents.The results, which can be …