# Mirabolic Langlands duality and the quantum Calogero–Moser system

Research paper by Thomas Nevins

Indexed on: 30 Oct '09Published on: 30 Oct '09Published in: Transformation Groups

#### 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.