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

Research output: Contribution to conference types › Conference Paper › peer-review

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 Bonnafé and Hohlweg.

Original language	English
Pages	509-520
Number of pages	12
Publication status	Published - 2010
Externally published	Yes
Event	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10 - San Francisco, CA, United States Duration: 2 Aug 2010 → 6 Aug 2010

Conference

Conference	22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10
Country/Territory	United States
City	San Francisco, CA
Period	2/08/10 → 6/08/10

!!!Keywords

Cayley graph
Hyperoctahedral group
Invariants of finite groups
Signed permutation module
Tensor algebras
Words

Cite this

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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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N2 - 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.

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.

KW - Cayley graph

KW - Hyperoctahedral group

KW - Invariants of finite groups

KW - Signed permutation module

KW - Tensor algebras

KW - Words

UR - https://www.scopus.com/pages/publications/84860505686

M3 - Conference Paper

AN - SCOPUS:84860505686

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EP - 520

T2 - 22nd International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'10

Y2 - 2 August 2010 through 6 August 2010

ER -

Words and noncommutative invariants of the hyperoctahedral group

Abstract

Conference

!!!Keywords

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Cite this