Seiberg-Witten differentials on the Hitchin base

In this note we describe explicitly, in terms of Lie theory and cameral data, the covariant (Gauss–Manin) derivative of the Seiberg–Witten differential defined on the weight-one variation of Hodge structures that exists on a Zariski open subset of the base of the Hitchin fibration. Dedicated to Tony Pantev on the occasion of his 60th birthday.