### Abstract

Original language | English |
---|---|

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

### Cite this

**Localization of quantum biequivariant Ɗ-modules and q–W algebras.** / Sevastyanov, A.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 113, no. 5, pp. 583-626. https://doi.org/10.1112/plms/pdw041

}

TY - JOUR

T1 - Localization of quantum biequivariant Ɗ-modules and q–W algebras

AU - Sevastyanov, A.

N1 - The author is grateful to Y. Kremnizer for useful discussions and to the referee for careful reading of the manuscript.

PY - 2016/11

Y1 - 2016/11

N2 - 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.

AB - 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.

KW - D–module

KW - W–algebra

KW - quantum group

U2 - 10.1112/plms/pdw041

DO - 10.1112/plms/pdw041

M3 - Article

VL - 113

SP - 583

EP - 626

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 5

ER -