Cohomological Hall algebras and character varieties
Algebraic Geometry
2016-05-17 v3 High Energy Physics - Theory
Quantum Algebra
Representation Theory
Abstract
In this paper we investigate the relationship between twisted and untwisted character varieties via a specific instance of the Cohomological Hall algebra for moduli of objects in 3-Calabi-Yau categories introduced by Kontsevich and Soibelman. In terms of Donaldson--Thomas theory, this relationship is completely understood via the calculations of Hausel and Villegas of the E polynomials of twisted character varieties and untwisted character stacks. We present a conjectural lift of this relationship to the cohomological Hall algebra setting.
Keywords
Cite
@article{arxiv.1504.00352,
title = {Cohomological Hall algebras and character varieties},
author = {Ben Davison},
journal= {arXiv preprint arXiv:1504.00352},
year = {2016}
}
Comments
Slight improvements picked up while editing for publication. To appear in IJM special volume for proceedings of VBAC 2014