Words and noncommutative invariants of the hyperoctahedral group

Anouk Bergeron-Brlek

Words and noncommutative invariants of the hyperoctahedral group

Anouk Bergeron-Brlek

York University Toronto

Résultats de recherche: Contribution à une conférence › Compte-rendu de conférence › Revue par des pairs

Résumé

Let Bn be the hyperoctahedral group acting on a complex vector space V. We present a combinatorial method to decompose the tensor algebra T(V) on V into simple modules via certain words in a particular Cayley graph of B _n. We then give combinatorial interpretations for the graded dimension and the number of free generators of the subalgebra T(V)B _n of invariants of B _n, in terms of these words, and make explicit the case of the signed permutation module. To this end, we require a morphism from the Mantaci-Reutenauer algebra onto the algebra of characters due to Bonnafé and Hohlweg.

langue originale	Anglais
Pages	509-520
Nombre de pages	12
état	Publié - 2010
Modification externe	Oui
Evénement	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, Etats-Unis Durée: 2 août 2010 → 6 août 2010

Conférence

Conférence	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Pays/Territoire	Etats-Unis
La ville	San Francisco, CA
période	2/08/10 → 6/08/10

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Contient cette citation

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abstract = "Let Bn be the hyperoctahedral group acting on a complex vector space V. We present a combinatorial method to decompose the tensor algebra T(V) on V into simple modules via certain words in a particular Cayley graph of B n. We then give combinatorial interpretations for the graded dimension and the number of free generators of the subalgebra T(V)B n of invariants of B n, in terms of these words, and make explicit the case of the signed permutation module. To this end, we require a morphism from the Mantaci-Reutenauer algebra onto the algebra of characters due to Bonnaf{\'e} and Hohlweg.",

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AB - Let Bn be the hyperoctahedral group acting on a complex vector space V. We present a combinatorial method to decompose the tensor algebra T(V) on V into simple modules via certain words in a particular Cayley graph of B n. We then give combinatorial interpretations for the graded dimension and the number of free generators of the subalgebra T(V)B n of invariants of B n, in terms of these words, and make explicit the case of the signed permutation module. To this end, we require a morphism from the Mantaci-Reutenauer algebra onto the algebra of characters due to Bonnafé and Hohlweg.

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KW - Hyperoctahedral group

KW - Invariants of finite groups

KW - Signed permutation module

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