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 |
|---|---|
| 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 Sept 2016 |
| DOIs | |
| Publication status | Published - Nov 2016 |
Bibliographical note
The author is grateful to Y. Kremnizer for useful discussions and to thereferee for careful reading of the manuscript.
Keywords
- D–module
- W–algebra
- quantum group
