Free Divisors and Duality for $\mathcal D$-Modules

The relationship between $\mathcal D$-modules and free divisors was studied in the general setting by L. Narváez and F. J. Calderón. Using the ideas of their works, we prove in this article a new duality formula between two $\mathcal D$-modules associated to a class of free divisors on $\mathbb C^n$ and give some applications.