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Inclusion d'algèbres de Hecke et nombres de décomposition

Abstract : This thesis is divided into three parts. The first one deals with the commutator formula of a group with a split BN-pair. We show that under a condition, say "weak condition of Lévi", this formula holds. In the second part, we study the conservation of the unitriangular shape from the decomposition matrix of a module over a graded algebra to the decomposition matrix of the restriction of this module over the algebra that makes the grading and conversely. The results apply for cellular algebras endowed with other combinatorial properties among which the Ariki-Koike algebras. The last part is about the conjecture of Gruber-Hiss for decomposition numbers of Hecke algebras of type B and D. We generalize this conjecture and prove it for the decomposition numbers of the algebras of complex reflections groups. Then we study what are the obstructions to generalize the methods used in this proof from group algebras to Hecke algebras (of type B and D). Finally, we give a natural condition about filtrations of Specht modules under which the conjecture holds. In the appendix, there are numerical examples, using gap programs, to illustrate the third part.
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Contributor : Gwenaelle Rassemusse Genet <>
Submitted on : Wednesday, July 7, 2004 - 8:58:39 AM
Last modification on : Tuesday, December 1, 2020 - 2:34:03 PM
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  • HAL Id : tel-00006398, version 1



Gwenaelle Rassemusse Genet. Inclusion d'algèbres de Hecke et nombres de décomposition. Mathématiques [math]. Université Paris-Diderot - Paris VII, 2004. Français. ⟨tel-00006398⟩



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