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 \(m-\varepsilon \) to \(m+\varepsilon \) for small \(\varepsilon >0\), 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.
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The research of E.G. was partially supported by the Grants DMS-1559338, DMS-1403560, RFBR-13-01-00755 and Russian Academic Excellence Project 5-100. The research of A.N. was partially supported by the Grant DMS-1600375.
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Gorsky, E., Neguț, A. Infinitesimal change of stable basis. Sel. Math. New Ser. 23, 1909–1930 (2017). https://doi.org/10.1007/s00029-017-0327-5
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DOI: https://doi.org/10.1007/s00029-017-0327-5