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Infinitesimal change of stable basis


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=ab 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 Uqgl^ 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.

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