English

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

Mathematical Physics 2014-01-16 v2 High Energy Physics - Theory math.MP Exactly Solvable and Integrable Systems

Abstract

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.

Keywords

Cite

@article{arxiv.1306.3072,
  title  = {The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints},
  author = {Johan van de Leur},
  journal= {arXiv preprint arXiv:1306.3072},
  year   = {2014}
}
R2 v1 2026-06-22T00:33:14.312Z