Singular localization of $\mathfrak{g}$-modules and applications to representation theory

Erik Backelin; Kobi Kremnitzer

doi:10.4171/jems/570

JournalsjemsVol. 17, No. 11pp. 2763–2787

Singular localization of $g$ -modules and applications to representation theory

Erik Backelin
Universidad de los Andes, Bogota, Colombia
Kobi Kremnitzer
University of Oxford, UK

$Singular localization of $\mathfrak{g}$-modules and applications to representation theory cover$

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Abstract

We prove a singular version of Beilinson–Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case settled by [BMR06]. We apply this theory to translation functors, singular blocks in the Bernstein–Gelfand–Gelfand category O and Whittaker modules.

Cite this article

Erik Backelin, Kobi Kremnitzer, Singular localization of $g$ -modules and applications to representation theory. J. Eur. Math. Soc. 17 (2015), no. 11, pp. 2763–2787

DOI 10.4171/JEMS/570