Algebra Seminar

In type A, nilpotent orbits are parametrized by partitions, and the singularities of their closures can be studied using transverse Slodowy slices. The classical work of Kraft and Procesi describes the minimal singularities of nilpotent orbit closures through simultaneous row and column removals.

 

In this talk, we study codimension-4 singularities in nilpotent orbit closures, where intermediate orbits may occur, using Maffei's realization of nilpotent Slodowy slices as Nakajima quiver varieties. We also construct quiver-variety involutions realizing Lie algebra anti-involutions and describe their fixed-point loci as singular Lagrangian subvarieties. These Lagrangians are closely related to the geometric classification of Harish-Chandra modules over quantizations of nilpotent orbits.