Equivariant K-theory of Hilbert schemes via shuffle algebra
By Boris Feigin, A. Tsymbaliuk. 2009
184 citations recorded by the source corpus.
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,...].
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1baef6bcc963f3531159b31f834a239758d57b7b
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Citations in the corpus
- Heisenberg categorification and Hilbert schemes (2010, methodology): “(We also note here that in the special case when S DC2 a natural C -action together with localization techniques have already been used to define Heisenberg algebra actions on localized equivariant K-theory; see [8], [25]).”
- Drinfeld realization of the elliptic Hall algebra (2010, result): “Finally, the algebra E (and the presentation given in Theorem 4) also appears in recent work of Feigin, Feigin, Jimbo, Miwa and Mukhin (see [5, 6, 9]) where its representation theory is studied.”