Exotic symmetric space over a finite field, II

This paper is the second part of the papers in the same title. In this paper, we prove a conjecture of Achar-Henderson, which asserts that the Poincare polynomials of the intersection cohomology complex associated to the closure of Sp_{2n}-orbits in the Kato's exotic nilpotent cone coincide with the modified Kostka polynomials indexed by double partitions, introduced by the first author. Actually this conjecture was recently proved by Kato by a different method. Our approach is based on the theory of character sheaves on the exotic symmetric space.