The nilpotent orbits of a Lie algebra play a central role in modern representation theory notably cropping up in the Springer correspondence and the fundamental lemma. Their behaviour when the base field is algebraically closed is well understood, however the p-adic case which arises in the study of admissible representations of p-adic groups is considerably more subtle. Their classification was only settled in the late 90s when Barbasch and Moy ('97) and Debacker (’02) developed an ‘affine Bala-Carter’ theory using the Bruhat-Tits building. In this talk we combine this work with work by Sommers and McNinch to provide a parameterisation of nilpotent orbits over a maximal unramified extension of a p-adic field in terms of so called dual Springer parameters and outline an application of this result to wavefront sets.
