Bernstein-Sato polynomials for maximal minors and sub-maximal Pfaffians

We determine the Bernstein-Sato polynomials for the ideal of maximal minors of a generic m×n matrix, as well as for that of sub-maximal Pfaffians of a generic skew-symmetric matrix of odd size. As a corollary, we obtain that the Strong Monodromy Conjecture holds in these two cases.