W-Constraints for the Total Descendant Potential of a Simple Singularity
Quantum Algebra
2019-02-20 v1 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
Simple, or Kleinian, singularities are classified by Dynkin diagrams of type ADE. Let g be the corresponding finite-dimensional Lie algebra, and W its Weyl group. The set of g-invariants in the basic representation of the affine Kac-Moody algebra g^ is known as a W-algebra and is a subalgebra of the Heisenberg vertex algebra F. Using period integrals, we construct an analytic continuation of the twisted representation of F. Our construction yields a global object, which may be called a W-twisted representation of F. Our main result is that the total descendant potential of the singularity, introduced by Givental, is a highest weight vector for the W-algebra.
Keywords
Cite
@article{arxiv.1203.3414,
title = {W-Constraints for the Total Descendant Potential of a Simple Singularity},
author = {Bojko Bakalov and Todor Milanov},
journal= {arXiv preprint arXiv:1203.3414},
year = {2019}
}
Comments
61 pages, 2 figures