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

TL;DR

This paper computes the based rings of specific two-sided cells in an affine Weyl group of type B_3 and verifies Lusztig's conjecture on their structure, focusing on the unipotent class in Sp_6(C).

Contribution

It provides explicit calculations of based rings for certain two-sided cells and confirms Lusztig's conjecture in this context, advancing understanding of affine Weyl group structures.

Findings

Computed based rings for two-sided cells in B_3

Verified Lusztig's conjecture on based ring structures

Enhanced understanding of unipotent class in Sp_6(C)

Abstract

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