On Nilpotent Orbits of SL n and Sp2n over a Local Non-Archimedean Field

Abstract

We relate the partition-type parametrization of rational (arithmetic) nilpotent adjoint orbits of the classical groups SL n and Sp2n over local non-Archimedean fields with a parametrization, introduced by DeBacker in 2002, which uses the associated Bruhat-Tits building to relate the question to one over the residue field.