Geodesic
On the Hopf algebra of noncommutative symmetric functions in superspace
Diego Arcis1 ; Camilo González2 ; Sebastián Márquez3
1Universidad de La Serena
2Universidad de Concepción
3Universidad Autónoma de Chile
The electronic journal of combinatorics, Tome 31 (2024) no. 3
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We study the combinatorial Hopf algebra of noncommutative symmetric functions in superspace sNSym, introduced by Fishel, Lapointe and Pinto. We introduce a family of primitive elements of sNSym and extend the noncommutative elementary and power sum functions to superspace. Then, we give formulas relating these families of functions. Also, we introduce noncommutative Ribbon Schur functions in superspace and provide an explicit formula for their product. We show that the dual basis of these functions is given by a family of the so–called fundamental quasisymmetric functions in superspace. This allows us to obtain an explicit formula for the coproduct of fundamental quasisymmetric functions in superspace. Additionally, by projecting the noncommutative Ribbon Schur functions in superspace, we define a new basis for the algebra of symmetric functions in superspace.
DOI : 10.37236/12295
Classification : 05E05, 16T05, 16T30, 81Q60, 81R12
Mots-clés : noncommutative Ribbon Schur functions, quasisymmetric functions in superspace

Diego Arcis  1   ; Camilo González  2   ; Sebastián Márquez  3

1 Universidad de La Serena
2 Universidad de Concepción
3 Universidad Autónoma de Chile 
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     author = {Diego Arcis and Camilo Gonz\'alez and Sebasti\'an M\'arquez},
     title = {On the {Hopf} algebra of noncommutative symmetric functions in superspace},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {3},
     doi = {10.37236/12295},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/12295/}
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Diego Arcis; Camilo González; Sebastián Márquez. On the Hopf algebra of noncommutative symmetric functions in superspace. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12295

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