The \({\mathbb {A}}_{q,t}\) algebra and parabolic flag Hilbert schemes

  • Erik CarlssonEmail author
  • Eugene Gorsky
  • Anton Mellit


The earlier work of the first and the third name authors introduced the algebra \({\mathbb {A}}_{q,t}\) and its polynomial representation. In this paper we construct an action of this algebra on the equivariant K-theory of certain smooth strata in the flag Hilbert scheme of points on the plane. In this presentation, the fixed points of the torus action correspond to generalized Macdonald polynomials, and the matrix elements of the operators have an explicit presentation.



The authors would like to thank Mikhail Bershtein, Andrei Neguț and Monica Vazirani for the useful discussions. The work of E. G. was partially supported by the NSF grants DMS-1559338 and DMS-1700814, Russian Academic Excellence Project 5-100 and RSF-16-11-10160. The work of A. M. was supported by the Advanced Grant “Arithmetic and Physics of Higgs moduli spaces” No. 320593 of the European Research Council and by the START-Project Y963-N35 of the Austrian Science Fund.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Faculty of MathematicsUniversity of ViennaViennaAustria

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