Open Access
Winter 2011 Equivariant K-theory of Hilbert schemes via shuffle algebra
B. L. Feigin, A. I. Tsymbaliuk
Kyoto J. Math. 51(4): 831-854 (Winter 2011). DOI: 10.1215/21562261-1424875


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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B. L. Feigin. A. I. Tsymbaliuk. "Equivariant K-theory of Hilbert schemes via shuffle algebra." Kyoto J. Math. 51 (4) 831 - 854, Winter 2011.


Published: Winter 2011
First available in Project Euclid: 10 November 2011

zbMATH: 1242.14006
MathSciNet: MR2854154
Digital Object Identifier: 10.1215/21562261-1424875

Primary: 16GXX

Rights: Copyright © 2011 Kyoto University

Vol.51 • No. 4 • Winter 2011
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