no. 1
Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
Bonnafé, Cédric1; Hohlweg, Christophe2
1 Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France)
2 The Fields Institute 222 College Street Toronto, Ontario M5T 3J1 (Canada)
Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 131-181.

We construct a subalgebra Σ ′ (W n ) of dimension 2·3 n-1 of the group algebra of the Weyl group W n of type B n containing its usual Solomon algebra and the one of 𝔖 n : Σ ′ (W n ) is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras Σ ′ (W n )→ZIrr(W n ). Jöllenbeck’s construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to W n . In an appendix, P. Baumann and C. Hohlweg present in an explicit and combinatorial way the relation between this construction of the irreducible characters of W n and that of W. Specht.

Nous construisons une sous-algèbre Σ ′ (W n ) de dimension 2·3 n-1 de l’algèbre du groupe de Weyl W n de type B n contenant son algèbre de Solomon usuelle ainsi que celle de 𝔖 n  : Σ ′ (W n ) n’est autre que l’algèbre de Mantaci-Reutenauer mais notre point de vue nous permet de construire un morphisme d’algèbres surjectif Σ ′ (W n )→ZIrr(W n ). La construction de Jöllenbeck des caractères irréductibles de 𝔖 n à partir des classes d’équivalence coplaxique se transpose alors à W n . Un appendice à cet article, écrit par P. Baumann et C. Hohlweg, donne le lien combinatoire explicite entre cette construction des caractères irréductibles de W n et celle obtenue par W. Specht en 1932.

DOI: 10.5802/aif.2176
Classification: 05E15
Keywords: descent algebra, hyperoctahedral group, coplactic algebra
Mot clés : algèbre de descente, groupe hyperoctaédral, algèbre coplaxique

Bonnafé, Cédric 1; Hohlweg, Christophe 2

1 Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France)
2 The Fields Institute 222 College Street Toronto, Ontario M5T 3J1 (Canada) 
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Bonnafé, Cédric; Hohlweg, Christophe. Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups. Annales de l'Institut Fourier, Volume 56 (2006) no. 1, pp. 131-181. doi : 10.5802/aif.2176. https://aif.centre-mersenne.org/articles/10.5802/aif.2176/

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