On Generalized Cells in Affine Weyl Groups Original Research Article

We determine the lowest generalized two-sided cell for affine Weyl groups. We show that it consists of at most W0 generalized left cells, whereW0denotes the corresponding finite Weyl group. For parameters coming from graph automorphisms, we prove that this bound is exact. For such parameters, we also characterize all generalized left cells for finite and affine Weyl groups.