Differential operators and Cherednik algebras

V. Ginzburg, I. Gordon, J. T. Stafford

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction [GS1]; the other involving quantum hamiltonian reduction of an algebra of differential operators [GG]. In this paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a naturally defined geometric twist functor on D-modules with the shift functor for the Cherednik algebra. That enables us to give a direct and relatively short proof of the key result [GS1, Theorem 1.4] without recourse to Haiman's deep results on the n! theorem [Ha1]. We also show that the characteristic cycles defined independently in these two approaches are equal, thereby confirming a conjecture from [GG]. © 2009 Birkhäuser Verlag Basel/Switzerland.
    Original languageEnglish
    Pages (from-to)629-666
    Number of pages37
    JournalSelecta Mathematica
    Volume14
    Issue number3-4
    DOIs
    Publication statusPublished - May 2009

    Keywords

    • Characteristic varieties
    • Cherednik algebra
    • Hilbert scheme

    Fingerprint

    Dive into the research topics of 'Differential operators and Cherednik algebras'. Together they form a unique fingerprint.

    Cite this