Nilpoten Conjugacy Classes of Reductive p-adic Lie Algebras and Definability in Pas's Language

We will study the following question: Are nilpotent conjugacy classes of reductive Lie algebras over p-adic fields definable by a formula in Pas's language. We answer in the affirmative in three cases: special orthogonal Lie algebras so(n) for n odd, special linear Lie algebra sl(3) and the exceptional Lie algebra G2 over p-adic fields. The nilpotent conjugacy classes in these three cases have been parameterized by Waldspurger (so(n)) and S. DeBacker(sl(3), G2). For sl (3) and G2 we are required to extend Pas's language by a finite number of symbols