Uniqueness Theorem of W-Constraints for Simple Singularities

In a recent paper, Bakalov and Milanov (Compositio. Math. 149:840-888, 2013) proved that the total descendant potential of a simple singularity satisfies the W-constraints, which come from the W-algebra of the lattice vertex algebra associated with the root lat- tice of this singularity and a twisted module of the vertex algebra. In the present paper, we prove that the solution of these W-constraints is unique up to a constant factor, as conjectured by Bakalov and Milanov in their paper. Mathematics Subject Classification (2010). Primary 53D45; Secondary 17B69, 32S30, 81R10.