Kazhdan-Lusztig cells in the affine Weyl groups of rank 2

TL;DR

This paper classifies Kazhdan-Lusztig cells in affine Weyl groups of rank 2 and confirms the semicontinuity conjecture for these cases, advancing understanding of their algebraic structure.

Contribution

It provides explicit partitions into Kazhdan-Lusztig cells for affine Weyl groups of types B2 and G2, and verifies the semicontinuity conjecture for these groups.

Findings

Explicit cell partitions for affine Weyl groups of types B2 and G2.

Validation of the semicontinuity conjecture in these cases.

Abstract

In this paper we determine the partition into Kazhdan-Lusztig cells of the affine Weyl groups of type $\tB_{2}$ and $\tG_{2}$ for any choice of parameters. Using these partitions we show that the semicontinuity conjecture of Bonnaf\'e holds for these groups.