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. Dans-la-première,-nous-nous-intéressons-À-la-formule-du-commutateur-d-'un-groupe-admettant-une-bn-paire-scindée, Nous montrons que sous une condition dite "condition de Lévi faible", le groupe vérifie cette formule Dans la seconde partie, nous étudions la conservation de la forme unitriangulaire lors du passage d'une matrice de décomposition d'un module sur une algèbre graduée à la matrice de décomposition de la restriction de ce module sur l'algèbre effectuant la graduation et vice-versa. Nous verrons des applications pour des algèbres cellulaires pourvues également d'autres propriétés combinatoires, notamment des algèbres de Ariki-Koike. Nous terminons par une partie traitant de la conjecture de J. Gruber et G. Hiss pour les nombres de décomposition des algèbres de Hecke de type B et D. Nous généralisons et prouvons cette conjecture dans le cas des algèbres de groupes de réflexions complexes. Puis nous observons quels sont les problèmes de la généralisation des méthodes utilisées lors du passage des algèbres de groupes aux algèbres de Hecke (de type B et D) Enfin, nous donnons une condition naturelle sur des filtrations de modules de Specht, sous laquelle la conjecture est satisfaite. En annexe, se trouvent des exemples numériques issus de programmes informatiques illustrant la troisième partie. DISCIPLINE : mathématiques MOTS -CLÉS : formule du commutateur -(B,N)-paire scindée matrice de décomposition unitriangulaire -algèbre graduée -théorie de Clifford -algèbre cellulaire -algèbre de Hecke -conjecture de Gruber-Hiss -nombres de