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

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 Bonnafé holds for these groups.

21 pages, 4 tables, 13 figures. Section 3 has been completely rewritten. The new version also contains some minor corrections