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On the lowest two-sided cell in affine Weyl groups

Jeremie Guilhot
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Abstract

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.

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Jeremie Guilhot. 2008-09-23. On the lowest two-sided cell in affine Weyl groups. https://arxiv.org/abs/math/0703764

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