Cohomological Hall algebras and character varieties

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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.
Original languageEnglish
JournalInternational Journal of Mathematics
Issue number07
Publication statusPublished - 28 Jun 2016


  • math.AG
  • hep-th
  • math.QA
  • math.RT
  • 14F05, 14H81

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