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Singular localization of 𝔤 -modules and applications to representation theory

Erik Backelin, Kobi Kremnitzer (2015)

Journal of the European Mathematical Society

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.

Singular Poisson-Kähler geometry of certain adjoint quotients

Johannes Huebschmann (2007)

Banach Center Publications

The Kähler quotient of a complex reductive Lie group relative to the conjugation action carries a complex algebraic stratified Kähler structure which reflects the geometry of the group. For the group SL(n,ℂ), we interpret the resulting singular Poisson-Kähler geometry of the quotient in terms of complex discriminant varieties and variants thereof.

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