The based rings of two-sided cells in an affine Weyl group of type $\tilde B_3$, II

Abstract: We compute the based rings of two-sided cells corresponding to the unipotent classes in $Sp_6(\mathbb C)$ with Jordan blocks (33), (411), (222) respectively. The results for the first two two-sided cells also verify Lusztig's conjecture on the structure of the based rings of two-sided cells of an affine Weyl group. The result for the last two-sided cell partially suggests a modification of Lusztig's conjecture on the structure of the based rings of two-sided cells of an affine Weyl group.