Heisenberg action in the equivariant Ktheory of Hilbert schemes via Shuffle Algebra
Abstract
In this paper we construct the action of DingIohara and shuffle algebras in the sum of localized equivariant Kgroups 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 Kgroups. 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,...].
 Publication:

arXiv eprints
 Pub Date:
 April 2009
 DOI:
 10.48550/arXiv.0904.1679
 arXiv:
 arXiv:0904.1679
 Bibcode:
 2009arXiv0904.1679F
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 some typos fixed, the last 2 subsections added, 20 pages