Abstract

According to a famous result of Brieskorn and Slodowy, the generic singularity of the nilpotent cone of a simple complex Lie algebra {\mathfrak g} is a Kleinian singularity, of a type exactly corresponding to the type of {\mathfrak g}. In a series of papers in the early 1980s, Kraft and Procesi extended this result to arbitrary nilpotent orbit closures in classical simple Lie algebras. In particular, they established equivalences between singularities associated to various nilpotent orbits in classical Lie algebras, expressed in terms of the combinatorial data attached to each orbit.

This talk will relate the results of a recent project determining generic singularities of nilpotent orbit closures in exceptional type Lie algebras. Our work has uncovered a number of isolated singularities which do not occur in the classical types, some of which explain non-normality of certain nilpotent orbit closures. One of the singularities we obtain appears to be a new example of an isolated symplectic singularity.

This is joint work with Baohua Fu, Daniel Juteau and Eric Sommers.