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Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters

Abstract : Hecke algebras arise naturally in the representation theory of reductive groups over finite or p-adic fields. These algebras are specializations of Iwahori-Hecke algebras which can be defined in terms of a Coxeter group and a weight function without reference to reductive groups and this is the setting we are working in. Kazhdan-Lusztig cells play a crucial role in the study of Iwahori-Hecke algebras. The aim of this work is to study the Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. More precisely, we show that the Kazhdan-Lusztig polynomials of an affine Weyl group are invariant under ``long enough'' translations, we decompose the lowest two-sided cell into left cells and we determine the decomposition of the affine Weyl group of type G into cells for a whole class of weight functions.
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https://tel.archives-ouvertes.fr/tel-00300796
Contributor : Jeremie Guilhot <>
Submitted on : Sunday, July 20, 2008 - 1:01:23 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:12 PM
Long-term archiving on: : Monday, May 31, 2010 - 8:44:07 PM

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  • HAL Id : tel-00300796, version 1

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Jeremie Guilhot. Kazhdan-Lusztig cells in affine Weyl groups with unequal parameters. Mathematics [math]. Université Claude Bernard - Lyon I, 2008. English. ⟨tel-00300796⟩

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