### Abstract

We present a biequivariant version of Kremnizer–Tanisaki localization theorem for quantum DD-modules. We also obtain an equivalence between a category of finitely generated equivariant modules over a quantum group and a category of finitely generated modules over a q–W algebra which can be regarded as an equivariant quantum group version of Skryabin equivalence. The biequivariant localization theorem for quantum DD-modules together with the equivariant quantum group version of Skryabin equivalence yield an equivalence between a certain category of quantum biequivariant DD-modules and a category of finitely generated modules over a q–W algebra.

Original language | English |
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Pages (from-to) | 583-626 |

Number of pages | 44 |

Journal | Proceedings of the London Mathematical Society |

Volume | 113 |

Issue number | 5 |

Early online date | 27 Sep 2016 |

DOIs | |

Publication status | Published - Nov 2016 |

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### Keywords

- D–module
- W–algebra
- quantum group