Left cells in affine Weyl groups
We prove a property of left cells in certain crystallographic groups \(W\), by which we formulate an algorithm to find a representative set of left cells of \(W\) in any given two-sided cell (in the sense of Kazhdan-Lusztig). As an illustration, we apply this algorithm to the case when \(W\) is the affine Weyl group of type \(\widetilde F_4\). This algorithm has been used by several authors in the study of Kazhdan-Lusztig cells of \(W\).
affine Weyl group of type \(\widetilde F_4\)
scientific article; zbMATH DE number 589804
scientific article