On the lowest two-sided cell in affine Weyl groups

Jeremie Guilhot (1)

1 Algebre

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.

Domaines: Mathématiques [math]

Jeremie Guilhot. On the lowest two-sided cell in affine Weyl groups. Representation Theory, 2008, 12, pp.327-345. ⟨hal-01109363⟩