Invariants in non-commutative variables of the symmetric and hyperoctahedral groups

Anouk Bergeron-Brlek

Invariants in non-commutative variables of the symmetric and hyperoctahedral groups

Anouk Bergeron-Brlek

York University Toronto

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

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages	653-664
Number of pages	12
Publication status	Published - 2008
Externally published	Yes
Event	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08 - Valparaiso, Chile Duration: 23 Jun 2008 → 27 Jun 2008

Conference

Conference	20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08
Country/Territory	Chile
City	Valparaiso
Period	23/06/08 → 27/06/08

!!!Keywords

Hopf algebra
Invariants
Non-commutative variables
Symmetric function

Cite this

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title = "Invariants in non-commutative variables of the symmetric and hyperoctahedral groups",

abstract = "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.",

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AU - Bergeron-Brlek, Anouk

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - Hopf algebra

KW - Invariants

KW - Non-commutative variables

KW - Symmetric function

UR - https://www.scopus.com/pages/publications/84860472745

M3 - Conference Paper

AN - SCOPUS:84860472745

SP - 653

EP - 664

T2 - 20th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC'08

Y2 - 23 June 2008 through 27 June 2008

ER -

Invariants in non-commutative variables of the symmetric and hyperoctahedral groups

Abstract

Conference

!!!Keywords

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