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On the lowest two-sided cell in affine Weyl groups


Author: Jérémie Guilhot
Journal: Represent. Theory 12 (2008), 327-345
MSC (2000): Primary 20C08
DOI: https://doi.org/10.1090/S1088-4165-08-00334-8
Published electronically: October 9, 2008
MathSciNet review: 2448287
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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 $ \vert W_{0}\vert$ 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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Additional Information

Jérémie Guilhot
Affiliation: Department of Mathematical Sciences, King’s College, Aberdeen University, Aberdeen AB24 3UE, Scotland, United Kingdom\indent Université de Lyon, Université Lyon 1, Institut Camille Jordan, CNRS UMR 5208, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France
Address at time of publication: School of Mathematics and Statistics F07, The University of Sydney, NSW 2006, Australia
Email: guilhot@maths.usyd.edu.au

DOI: https://doi.org/10.1090/S1088-4165-08-00334-8
Received by editor(s): August 27, 2007
Published electronically: October 9, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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