# Fourier transform for quantum D-modules via the punctured torus mapping class group

@article{Brochier2017FourierTF,
title={Fourier transform for quantum D-modules via the punctured torus mapping class group},
author={Adrien Brochier and David A. Jordan},
journal={Quantum Topology},
year={2017},
volume={8},
pages={361-379}
}
• Published 7 March 2014
• Mathematics
• Quantum Topology
We construct a certain cross product of two copies of the braided dual $\tilde H$ of a quasitriangular Hopf algebra $H$, which we call the elliptic double $E_H$, and which we use to construct representations of the punctured elliptic braid group extending the well-known representations of the planar braid group attached to $H$. We show that the elliptic double is the universal source of such representations. We recover the representations of the punctured torus braid group obtained in arXiv…
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