1306.3072 (Johan van de Leur)

The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints    [PDF]

Johan van de Leur

The total descendent potential of 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 the 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.

View original: http://arxiv.org/abs/1306.3072