On Singular Localization of $\mathfrak{g}$-modules

Abstract

We prove a singular version of Beilinson-Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case done by \cite{BMR2}. We apply this theory to translation functors, singular blocks in the Bernstein-Gelfand-Gelfand category $\BGGcat$ and Whittaker modules.

22 pages, accepted for publication in JEMS

References in corpus (3)

• Noncommutative Counterparts of the Springer Resolution
• Singular blocks of parabolic category O and finite W-algebras
• Representations of semisimple Lie algebras in prime characteristic and noncommutative Springer resolution

Cited by in corpus (3)

• Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras
• Beilinson-Bernstein localization over the Harish-Chandra center
• Remarks on the derived center of small quantum groups