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

A. Sevastyanov

doi:10.1112/plms/pdw041

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

A. Sevastyanov

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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 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	https://doi.org/10.1112/plms/pdw041
Publication status	Published - Nov 2016

Keywords

D–module
W–algebra
quantum group

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Alexey Sevostyanov
- School of Natural & Computing Sciences, Mathematical Science - Reader
- Mathematical Sciences (Research Theme)
Person: Academic

Cite this

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title = "Localization of quantum biequivariant Ɗ-modules and q–W algebras",

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.",

keywords = "D–module, W–algebra, quantum group",

author = "A. Sevastyanov",

note = "The author is grateful to Y. Kremnizer for useful discussions and to the referee for careful reading of the manuscript.",

year = "2016",

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doi = "10.1112/plms/pdw041",

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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 -

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

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Alexey Sevostyanov

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