Mirabolic Langlands duality and the quantum Calogero-Moser system

Thomas Nevins

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arXiv · 0804.4170

Mirabolic Langlands duality and the quantum Calogero-Moser system

Thomas Nevins

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Abstract

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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Thomas Nevins. 2009-08-26. Mirabolic Langlands duality and the quantum Calogero-Moser system. https://arxiv.org/abs/0804.4170

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