  The total descendent potential of a simple singularity satisfies the
Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it
is also a highest weight vector for the corresponding W-algebra. This was used
by Liu, Yang and Zhang to prove its uniqueness. We construct this principal
hierarchy of type D in a different way, viz. as a reduction of some DKP
hierarchy. This gives a Lax type and a Grassmannian formulation of this
hierarchy. We show in particular that the string equation induces a large part
of the W constraints of Bakalov and Milanov. These constraints are not only
given on the tau function, but also in terms of the Lax and Orlov-Schulman
operators.
