LGRT 1621
Among the nilpotent orbits in a simple Lie algebra are the special nilpotent orbits, which possess an order-reversing involution to the special orbits in the Langlands dual Lie algebra. In this talk, I'll give the classification of the isomorphism types of Slodowy slices between adjacent special orbits, and then discuss a duality between isomorphism types under the involution, generalizing an observation of Kraft-Procesi for type A. This talk is based on the preprint (https://arxiv.org/abs/2310.00521), joint with Paul Levy and Daniel Juteau.