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We relate the partition-type parametrization of rational (arithmetic)nilpotent adjoint orbits of the split classical groups $SL_n$ and $Sp_{2n}$over local non-Archimedean fields with a parametrization, introduced byDeBacker in 2002, which uses the associated Bruhat-Tits building to relate thequestion to one over the residue field.

On Rational Nilpotent Orbits of $SL_{n}$ and $Sp_{2n}$ over a Local Non-Archimedean Field