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