#####
Séminaire Lotharingien de Combinatoire, 78B.1 (2017), 12 pp.

# Eugene Gorsky and Andrei Negut

# 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
**R**. When *m* = *a*/*b* is rational, we study the change of
stable basis 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.

Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.

The following versions are available: