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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