The relative hermitian duality functor

Abstract

We extend to the category of relative regular holonomic modules on a manifold $X$, parametrized by a curve $S$, the Hermitian duality functor (or conjugation functor) of Kashiwara. We prove that this functor is an equivalence with the similar category on the conjugate manifold $\overline X$, parametrized by the same curve. As a byproduct we introduce the notion of regular holonomic relative distribution.