The Based Rings of Two-sided cells in an Affine Weyl group of type $\tilde B_3$, IV

TL;DR

This paper computes the based ring of a specific two-sided cell in an affine Weyl group of type B3, confirming Lusztig's conjecture on the structure of such rings.

Contribution

It provides an explicit computation of the based ring for a particular two-sided cell in an affine Weyl group of type B3, verifying a key conjecture by Lusztig.

Findings

Computed the based ring for the two-sided cell in type B3

Verified Lusztig's conjecture on based ring structures

Enhanced understanding of affine Weyl group cell structures

Abstract

We compute the based ring of two-sided cell corresponding to the unipotent class in $Sp_6(\mathbb C)$ 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.