The Based Rings of Two-sided cells in an Affine Weyl group of type ${\tilde{B}}_3$, III

We compute the based rings of two-sided cells corresponding to the unipotent class in $S{p}_6(\mathbb{C})$ with Jordan blocks (2211). The results also verify Lusztig’s conjecture on the structure of the based rings of the two-sided cells of an affine Weyl group.