English

Counting stringy points on a family of character varieties

Algebraic Geometry 2024-11-11 v1 Representation Theory

Abstract

We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy the Betti Topological Mirror Symmetry Conjecture of T. Hausel and M. Thaddeus, as well as a refinement regarding isotypic components. Our proof is based on a Frobenius' type formula for Clifford's type settings and an analysis of it in a specific set-up related to regular wreath products with cyclic groups.

Keywords

Cite

@article{arxiv.2411.05563,
  title  = {Counting stringy points on a family of character varieties},
  author = {Lucas de Amorin and Martin Mereb},
  journal= {arXiv preprint arXiv:2411.05563},
  year   = {2024}
}