  In his work on the mathematical formulation of 2d quantum gravity Schwarz
established a rigidity result for Kac-Schwarz operators for the n-KdV
hierarchies. Later on, Adler and van Moerbeke as well as Fastr\'{e} obtained
different proofs of this result. We give yet another proof of the rigidity, one
that in fact holds for all Drinfeld-Sokolov hierarchies.
