Generalized descent algebra and construction of irreducible characters   of hyperoctahedral groups
  We construct a subalgebra of dimension $2.3^{n-1}$ of the group algebra of a Weyl group of type $B_n$ containing its Solomon descent's algebra but also the Solomon's descent algebra of the symmetric group. This lead us to a construction of the irreducible characters of the hyperoctahedral groups by using a generalized plactic equivalence. 
Cedric Bonnafe, Christophe Hohlweg (IRMA)