Infinitesimal change of stable basis

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∈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 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.