A Lie algebra action on the Chow ring of the Hilbert scheme of points of a K3 surface

We construct an action of the Neron–Severi part Looijenga–Lunts–Verbitsky Lie algebra on Chow ring Hilbert scheme points a K3 surface. This yields simplification Maulik and Negut’s proof that cycle class map is injective subring generated by divisor classes as conjectured Beauville. The key step in construction explicit formula for Lefschetz duals terms Nakajima operators. Our results also lead to monodromy schemes