The based rings of two-sided cells in an affine Weyl group of type ${\tilde{B}}_3$, II

We compute the based rings of two-sided cells corresponding to the unipotent classes in $S{p}_6(\mathbb{C})$ 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.