Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups

Cédric Bonnafé[1]; Christophe Hohlweg[2]

  • [1] Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France)
  • [2] The Fields Institute 222 College Street Toronto, Ontario M5T 3J1 (Canada)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 1, page 131-181
  • ISSN: 0373-0956

Abstract

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We construct a subalgebra Σ ′ ( W n ) of dimension 2 · 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 ) → 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 combinatorial way the relation between this construction of the irreducible characters of W n and that of W. Specht.

How to cite

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Bonnafé, Cédric, and Hohlweg, Christophe. "Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups." Annales de l’institut Fourier 56.1 (2006): 131-181. <http://eudml.org/doc/10137>.

@article{Bonnafé2006,
abstract = {We construct a subalgebra $\Sigma ^\{\prime\}(W_n)$ 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 $\{\mathfrak\{S\}\}_n$: $\Sigma ^\{\prime\}(W_n)$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $\Sigma ^\{\prime\}(W_n) \rightarrow \{\{\mathbf\{Z\}\}\}\{\mathrm\{Irr\}\}(W_n)$. 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 combinatorial way the relation between this construction of the irreducible characters of $W_n$ and that of W. Specht.},
affiliation = {Université de Franche-Comté Département de Mathématiques 16 route de Gray 25000 Besançon (France); The Fields Institute 222 College Street Toronto, Ontario M5T 3J1 (Canada); Université Louis Pasteur et CNRS Institut de recherche mathématique avancée 7 rue René Descartes 67084 Strasbourg Cedex (France)},
author = {Bonnafé, Cédric, Hohlweg, Christophe},
journal = {Annales de l’institut Fourier},
keywords = {descent algebra; hyperoctahedral group; coplactic algebra; descent algebras; hyperoctahedral groups; coplactic algebras; group algebras; Weyl groups; Solomon algebras; irreducible characters of symmetric groups; Specht modules},
language = {eng},
number = {1},
pages = {131-181},
publisher = {Association des Annales de l’institut Fourier},
title = {Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups},
url = {http://eudml.org/doc/10137},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Bonnafé, Cédric
AU - Hohlweg, Christophe
TI - Generalized descent algebra and construction of irreducible characters of hyperoctahedral groups
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 1
SP - 131
EP - 181
AB - We construct a subalgebra $\Sigma ^{\prime}(W_n)$ 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 ${\mathfrak{S}}_n$: $\Sigma ^{\prime}(W_n)$ is nothing but the Mantaci-Reutenauer algebra but our point of view leads us to a construction of a surjective morphism of algebras $\Sigma ^{\prime}(W_n) \rightarrow {{\mathbf{Z}}}{\mathrm{Irr}}(W_n)$. 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 combinatorial way the relation between this construction of the irreducible characters of $W_n$ and that of W. Specht.
LA - eng
KW - descent algebra; hyperoctahedral group; coplactic algebra; descent algebras; hyperoctahedral groups; coplactic algebras; group algebras; Weyl groups; Solomon algebras; irreducible characters of symmetric groups; Specht modules
UR - http://eudml.org/doc/10137
ER -

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