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

Abstract

We compute the based ring of two-sided cell corresponding to the unipotent class in $S{p}_6(\mathbb{C})$ with Jordan blocks (21111). The results also verify Lusztig's conjecture on the structure of the based rings of the two-sided cells of an affine Weyl group.