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

Anouk Bergeron-Brlek

doi:10.46298/dmtcs.3609

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

dmtcs:3609 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008) - https://doi.org/10.46298/dmtcs.3609

Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral GroupsConference paper

Authors: Anouk Bergeron-Brlek ¹

1 Department of Mathematics and Statistics [Toronto]

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.

https://doi.org/10.46298/dmtcs.3609

Source: HAL:hal-01185143v1

Volume: DMTCS Proceedings vol. AJ, 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008)

Section: Proceedings

Published on: January 1, 2008

Imported on: May 10, 2017

Keywords: 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]

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

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