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}
}