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

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