Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Abstract

We construct a subalgebra ∑′(Wn) of dimension 2 · 3n-1 of the group algebra of the Weyl group Wn of type Bn containing its usual Solomon algebra and the one of script G signn: ∑′(Wn) is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras ∑′(Wn) → ZIrr(W n). Jöllenbeck's construction of irreducible characters of the symmetric group by using the coplactic equivalence classes can then be transposed to Wn. 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 Wn and that of W. Specht.