# Equivariant K-theory of Hilbert schemes via shuffle algebra

@article{Feigin2011EquivariantKO, title={Equivariant K-theory of Hilbert schemes via shuffle algebra}, author={Boris Feigin and Alexander Tsymbaliuk}, journal={Journal of Mathematics of Kyoto University}, year={2011}, volume={51}, pages={831-854} }

In this paper we construct the action of Ding-Iohara and shuffle algebras in the sum of localized equivariant K-groups of Hilbert schemes of points on C^2. We show that commutative elements K_i of shuffle algebra act through vertex operators over positive part {h_i}_{i>0} of the Heisenberg algebra in these K-groups. Hence we get the action of Heisenberg algebra itself. Finally, we normalize the basis of the structure sheaves of fixed points in such a way that it corresponds to the basis of…

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