Abstract
The total descendent potential of a simple singularity satisfies the Kac{Waki- moto 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.
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