Cohomological Hall algebras and character varieties
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2015
- DOI:
- 10.48550/arXiv.1504.00352
- arXiv:
- arXiv:1504.00352
- Bibcode:
- 2015arXiv150400352D
- Keywords:
-
- Mathematics - Algebraic Geometry;
- High Energy Physics - Theory;
- Mathematics - Quantum Algebra;
- Mathematics - Representation Theory;
- 14F05;
- 14H81
- E-Print:
- Slight improvements picked up while editing for publication. To appear in IJM special volume for proceedings of VBAC 2014