Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cedric Bonnafe; Christophe Hohlweg

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Combinatorics 2008-07-07 v2

Authors: Cedric Bonnafe , Christophe Hohlweg

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.

Keywords

descent algebra hyperoctahedral group weyl group of type b irreducible character plactic equivalence group algebra

Cite

@article{arxiv.math/0409199,
  title  = {Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups},
  author = {Cedric Bonnafe and Christophe Hohlweg},
  journal= {arXiv preprint arXiv:math/0409199},
  year   = {2008}
}

Comments

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

Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Abstract

Keywords

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