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" $m\in \mathbb{R}$. When $m=\frac{a}{b}$ is rational, we study the change of stable matrix from slope $m-\epsilon$ to $m+\epsilon$ for small $\epsilon >0$, 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.

13 pages, 1 figure