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Selecta Mathematica

, Volume 23, Issue 3, pp 1909–1930 | Cite as

Infinitesimal change of stable basis

  • Eugene Gorsky
  • Andrei NeguțEmail author
Article

Abstract

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” \(m \in {\mathbb {R}}\). When \(m = \frac{a}{b}\) is rational, we study the change of stable matrix from slope \(m-\varepsilon \) to \(m+\varepsilon \) for small \(\varepsilon >0\), and conjecture that it is related to the Leclerc–Thibon conjugation in the q-Fock space for \(U_q\widehat{{\mathfrak {gl}}}_b\). 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.

Keywords

Stable and canonical bases Leclerc–Thibon involution Hilbert schemes 

Mathematics Subject Classification

17B37 

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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of MathematicsUC DavisDavisUSA
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Mathematics DepartmentMassachusetts Institute of TechnologyCambridgeUSA
  4. 4.Simion Stoilow Institute of MathematicsBucharestRomania

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