Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
classification
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algebradescentgroupcharactersconstructiongeneralizedgroupshyperoctahedral
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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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