# 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} }

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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