Let E be a finite dimensional vector space over an algebraic closure of a
finite field with a given linear action of a connected linear algebraic group K
and let E' be the dual space. A complex of l-adic sheaves on E is said to be
orbital if it is a simple perverse sheaf whose support is a single K-orbit. A
complex of l-adic sheaves on E is said to be biorbital if it is orbital and if
its Deligne Fourier transform is orbital on E'. In this paper we study examples
of biorbital complexes arising in the case where E is an eigenspace of a
semisimple automorphism of a reductive Lie algebra.

We consider the variety of nilpotent elements in the dual of the Lie algebra
of a reductive algebraic group over an algebraically closed field. We propose a
definition of a partition of this variety into smooth locally closed smooth
subvarieties indexed by the unipotent classes in the corresponding group over
complex numbers. We obtain explicit results in type A,C and D.