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arxiv: 1705.07491 · v1 · pith:VZZKE3UUnew · submitted 2017-05-21 · 🧮 math.RT

On cohomological Hall algebras of quivers : Yangians

Olivier Schiffmann , Eric Vasserot This is my paper
classification 🧮 math.RT
keywords quiveractionsalgebraalgebrascohomologicalcohomologyhallvarieties
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We consider the cohomological Hall algebra Y of a Lagrangian substack of the moduli stack of representations of the preprojective algebra of an arbitrary quiver Q, and its actions on the cohomology of quiver varieties. We conjecture that Y is equal, after a suitable extension of scalars, to the Yangian introduced by Maulik and Okounkov, and we construct an embedding of Y in the Yangian, intertwining the respective actions of both algebras on the cohomology of quiver varieties.

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  1. The R-matrix of the affine Yangian

    math.RT 2023-09 unverdicted novelty 7.0

    Proves existence of meromorphic R-matrices for affine Yangian representations in category O via a new difference equation and higher-order adjoint action, inducing identical rational R-matrices on highest-weight pairs.