Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Details Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

2004-09-13

arxiv.org/abs/math/0409199v2

Annales de l'Institut Fourier 56 (2008) 131-181

Mathematics

Combinatorics

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

Scientific paper

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.

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