# 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}
}
• Published 10 April 2009
• Mathematics
• Journal of Mathematics of Kyoto University
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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