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Cohomological Hall algebras of quivers and Yangians
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We construct an isomorphism between the preprojective cohomological Hall algebra of an arbitrary quiver and a positive half of the corresponding Maulik-Okounkov Yangian, which intertwines the respective actions on the cohomology of the Nakajima quiver varieties. We use this to prove a conjecture of Okounkov relating the character of the Maulik-Okounkov Lie algebra to Kac polynomials.
Forward citations
Cited by 3 Pith papers
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The loop-nilpotent cohomological Hall algebra
Loop-nilpotent CoHAs of tripled quivers are isomorphic to an explicit integral shuffle algebra, yielding generators, Coulomb-branch surjections, BPS characterizations, and a new Kac-polynomial formula.
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Cohomological Hall algebras of one-dimensional sheaves on surfaces and Yangians
The cohomological Hall algebra of curve-supported coherent sheaves on a Kleinian resolution is isomorphic to the completed positive half of the affine Yangian of the corresponding affine ADE Lie algebra.
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Comparison of Cohomological and K-theoretical Hall algebra
A comparison morphism from the K-theoretical Hall algebra to a twisted cohomological Hall algebra is derived from square roots of Todd classes and extended to symmetric quivers with potential.
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