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 in 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 U_q(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.

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Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology

Exts and the AGT relations