Nilpotent coadjoint orbits in small characteristic

Abstract

We show that the numbers of nilpotent coadjoint orbits in the dual of exceptional Lie algebra G2 in characteristic 3 and in the dual of exceptional Lie algebra F4 in characteristic 2 are finite. We determine the closure relation among nilpotent coadjoint orbits in the dual of Lie algebras of type B, C, F4 in characteristic 2 and in the dual of Lie algebra of type G2 in characteristic 3. In each case we give an explicit description of the nilpotent pieces in the dual defined in [2], which are in general unions of nilpotent coadjoint orbits, coincide with the earlier case-by-case definition in [11,26] in the case of classical groups and have nice properties independent of the characteristic of..