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Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé; Christophe Hohlweg — 2006

Annales de l’institut Fourier

We construct a subalgebra $Σ^{'} (W_{n})$ of dimension $2 \cdot 3^{n - 1}$ 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 $Σ^{'} (W_{n}) \to Z Irr (W_{n})$ . 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...

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The centers of gravity of the associahedron and of the permutahedron are the same.

Isometry classes of generalized associahedra.

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups