Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra

Details Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra Heisenberg action in the equivariant K-theory of Hilbert schemes via Shuffle Algebra

2009-04-10

arxiv.org/abs/0904.1679v1

Mathematics

Representation Theory

Scientific paper

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 Macdonald polynomials in the Fock space k[h_1,h_2,...].

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