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

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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 languageEnglish
Pages (from-to)583-626
Number of pages44
JournalProceedings of the London Mathematical Society
Volume113
Issue number5
Early online date27 Sep 2016
DOIs
Publication statusPublished - Nov 2016

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Keywords

  • D–module
  • W–algebra
  • quantum group

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