An explicit Chow-level lift of the Neron-Severi Looijenga-Lunts-Verbitsky Lie algebra action on Hilbert schemes of K3 surfaces is constructed via Nakajima operators.
Voisin, On the Chow ring of certain algebraic hyper-K¨ ahler manifol ds, Pure Appl
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A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface
An explicit Chow-level lift of the Neron-Severi Looijenga-Lunts-Verbitsky Lie algebra action on Hilbert schemes of K3 surfaces is constructed via Nakajima operators.