On the lowest two-sided cell in affine Weyl groups
Abstract
Description
Bremke and Xi determined the lowest two-sided cell for affine Weyl groups with unequal parameters and showed that it consists of at most |W_{0}| left cells where W_{0} is the associated finite Weyl group. We prove that this bound is exact. Previously, this was known in the equal parameter case and when the parameters were coming from a graph automorphism. Our argument uniformly works for any choice of parameters.
18 pages, 1 figure, final version (minor changes). To appear in Representation theory
18 pages, 1 figure, final version (minor changes). To appear in Representation theory