Infinitesimal change of stable basis

• Eugene Gorsky ^[1] ; Andrei Negut ^[2]
  1. [1] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  2. [2] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 3, 2017, págs. 1909-1930
• Idioma: inglés
• DOI: 10.1007/s00029-017-0327-5
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• Resumen

  • The purpose of this note is to study the Maulik–Okounkov K-theoretic stable basis for the Hilbert scheme of points on the plane, which depends on a “slope” m ∈ R. When m = a/b is rational, we study the change of stable matrix from slope m − ε to m + ε for small ε > 0, and conjecture that it is related to the Leclerc– Thibon conjugation in the q-Fock space for Uqglˆb. This is part of a wide framework of connections involving derived categories of quantized Hilbert schemes, modules for rational Cherednik algebras and Hecke algebras at roots of unity.