Counting Number Of F_q-Rational Points Of Nilpotent Orbits

Let G be a classical group of type A, B, C, or D over k=Fq where q is a power of the prime characteristic of k, and F a standard Frobenius morphism on G which can be defined naturally on g=Lie(G). In this paper, we clearly investigate the number of Fq- rational points|OF|for all nilpotent orbits in g under the adjoint action of G when the characteristic of k is bigger than 2 and give a concrete algorithm and formula for|OF|, also we give some examples to check our formula.