Singular localization of \(\mathfrak{g}\)-modules and applications to representation theory
type: Item
instance of: scholarly article
title: Singular localization of \(\mathfrak{g}\)-modules and applications to representation theory
zbMATH Open document ID: 1380.17006
DOI: 10.4171/JEMS/570
author: Erik Backelin
author: Kobi Kremnitzer
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2015-11-27T00:00:00Z
review text: This paper develops a singular version of Beilinson-Bernstein localization theory for a complex semisimple Lie algebra. The main result is a singular version of the localization theorem which connects Lie algebra modules having a prescribed (singular) central character with certain twisted differential operators. As an application, various known results are reproved. In particular, a theorem of Bernstein and S.~Gelfand which connects category \(\mathcal{O}\) to Harish-Chandra bimodules; and a theorem of Miličić and Soergel which connects category \(\mathcal{O}\) to a certain category of Whittaker modules.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 14F10
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 6514539
zbMATH Keywords: Lie algebra
zbMATH Keywords: localization
zbMATH Keywords: category \(\mathcal{O}\)
zbMATH Keywords: translation functor
zbMATH Keywords: singular block
zbMATH Keywords: Whittaker module
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/jems/570
OpenAlex ID: W2217393665
description: scientific article; zbMATH DE number 6514539