Mirabolic Langlands duality and the quantum Calogero-Moser system

Details Mirabolic Langlands duality and the quantum Calogero-Moser system Mirabolic Langlands duality and the quantum Calogero-Moser system

2008-04-25

arxiv.org/abs/0804.4170v3

Mathematics

Algebraic Geometry

final version; to appear in Transformation Groups

Scientific paper

We give a generic spectral decomposition of the derived category of twisted 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 quasi-coherent 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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