Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.
Factorisation quantum groups
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abstract
We develop vertex and factorisation algebra analogues of the theory of quasitriangular bialgebras. Analogously to the classical theory, we prove their categories of representations are controlled by spectral R-matrices. In the vertex algebra case this generalises previous notions due to Etingof-Kazhdan and Frenkel-Reshetikhin. Finally we give examples, including Borcherds twists and homology vertex algebras.
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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.