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Mirabolic Langlands duality and the quantum Calogero–Moser system

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Abstract

We give a generic spectral decomposition of the derived category of twisted \(\mathcal{D} \)-modules on a moduli stack of mirabolic vector bundles on a curve X in characteristic p: that is, we construct an equivalence with the derived category of quasicoherent sheaves on a moduli stack of mirabolic local systems on X. This equivalence may be understood as a tamely ramified form of the geometric Langlands equivalence. When X has genus 1, this equivalence generically solves (in the sense of noncommutative geometry) the quantum Calogero–Moser system.

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  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Thomas Nevins

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Nevins, T. Mirabolic Langlands duality and the quantum Calogero–Moser system. Transformation Groups 14, 931–983 (2009). https://doi.org/10.1007/s00031-009-9068-7

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