Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups

Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups

We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analogous to the algebra $Sym$ of the ordinary symmetric functions in commutative variables. We give formulaes for the product and coproduct on some of the analogues of the $Sym$ bases and exp...

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Bibliographic Details
Main Author: Anouk Bergeron-Brlek
Format: Article
Language:English
Published: Discrete Mathematics & Theoretical Computer Science 2008-01-01
Series:Discrete Mathematics & Theoretical Computer Science
Subjects:
invariants
symmetric function
non-commutative variables
hopf algebra
[math.math-co] mathematics [math]/combinatorics [math.co]
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
Online Access:https://dmtcs.episciences.org/3609/pdf
Description
Summary:We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analogous to the algebra $Sym$ of the ordinary symmetric functions in commutative variables. We give formulaes for the product and coproduct on some of the analogues of the $Sym$ bases and expressions for a shuffle product on $NCSym$. We also consider the invariants of the hyperoctahedral group in the non-commutative case and a state a few results.
ISSN:1365-8050

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