Classical type parabolic induction produces twisted Yetter-Drinfeld vertex modules for cohomological Hall algebras, including cases of dimension-zero sheaves on surfaces.
[Che] Cherednik, I.V., Factorizing particles on a half line and root systems , Theor
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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.