Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.
Cohomological Hall algebras and vertex algebras
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abstract
The moduli stack of representations of a quiver, or coherent sheaves on a proper curve, carries two structures on its cohomology: a Hall algebra and braided vertex coalgebra. We show that they are compatible, by developing a formulation of abelian localisation which works in the derived/singular setting. An application of these techniques gives an explicit formula for the cohomological Hall algebra products.
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Orthosymplectic modules of cohomological Hall algebras
Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.