Singularities of nilpotent orbit closures

Abstract

This is an expository article on the singularities of nilpotent orbit closures in simple Lie algebras over the complex numbers. It is slanted towards aspects that are relevant for representation theory, including Maffei's theorem relating Slodowy slices to Nakajima quiver varieties in type A. There is one new observation: the results of Juteau and Mautner, combined with Maffei's theorem, give a geometric proof of a result on decomposition numbers of Schur algebras due to Fang, Henke and Koenig.

30 pages. Version 2 has very minor modifications; final version, to appear in proceedings of the 5th Japanese-Australian Workshop on Real and Complex Singularities

References in corpus (6)

• Lectures on Nakajima's Quiver Varieties
• Diagram automorphisms of quiver varieties
• Correspondance de Springer modulaire et matrices de décomposition
• Modular Springer correspondence, decomposition matrices and basic sets
• Generic singularities of nilpotent orbit closures
• Comparing $G{L}_n$-Representations by Characteristic-Free Isomorphisms between Generalized Schur Algebras

Cited by in corpus (5)

• Vertex operator algebras, Higgs branches, and modular differential equations
• Quiver Subtractions
• Jet schemes of the closure of nilpotent orbits
• On the irreducibility of associated varieties of W-algebras
• Generic singularities of nilpotent orbit closures