# Représentations modulaires des algèbres de Hecke et des algèbres de Ariki-Koike

Abstract : Let $W$ be a finite Weyl group and let $H$ be the associated Hecke algebra defined over the ring $A:=Z[v,v^(-1)]$ where $v$ is an indeterminate. Let $K$ be the field of fractions of $A$ and let $\theta$ be a specialisation in a field $L$. We assume that the characteristic of $L$ is good''. Then, by using Lusztig's $a$-function, M.Geck and R.Rouquier have defined a canonical basic set'' $B$ which leads to the determination of the set $\Irr(H_L)$. The aim of this work is to find explicitly this set for all $W$ and for all $\theta$ and to extend these results to the case of Ariki-Koike algebras. As consequences, we obtain an algorithm for the computation of the decomposition matrices for Ariki-Koike algebras and a characterisation of the simple modules for some cyclotomic Hecke algebras of type $G(l,l,n)$.
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https://tel.archives-ouvertes.fr/tel-00006383
Contributor : Nicolas Jacon <>
Submitted on : Tuesday, July 6, 2004 - 10:28:01 AM
Last modification on : Tuesday, November 19, 2019 - 2:45:21 AM
Long-term archiving on: : Wednesday, September 12, 2012 - 4:30:09 PM

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• HAL Id : tel-00006383, version 1

### Citation

Nicolas Jacon. Représentations modulaires des algèbres de Hecke et des algèbres de Ariki-Koike. Mathématiques [math]. Université Claude Bernard - Lyon I, 2004. Français. ⟨tel-00006383⟩

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