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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