Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Abstract

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.

32 pages + un appendice par P. Baumann et C. Hohlweg ("Comparison with Specht construction")