Kyoto Journal of Mathematics

Equivariant K-theory of Hilbert schemes via shuffle algebra

B. L. Feigin and A. I. Tsymbaliuk

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In this paper we construct the action of Ding-Iohara and shuffle algebras on the sum of localized equivariant K-groups of Hilbert schemes of points on C2. We show that commutative elements Ki of shuffle algebra act through vertex operators over the positive part {hi}i>0 of the Heisenberg algebra in these K-groups. Hence we get an 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 Macdonald polynomials in the Fock space C[h1,h2,].

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Kyoto J. Math. Volume 51, Number 4 (2011), 831-854.

First available in Project Euclid: 10 November 2011

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Primary: 16Gxx: Representation theory of rings and algebras


Feigin, B. L.; Tsymbaliuk, A. I. Equivariant K -theory of Hilbert schemes via shuffle algebra. Kyoto J. Math. 51 (2011), no. 4, 831--854. doi:10.1215/21562261-1424875.

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