Work

On the Hopf Algebra of Noncommutative Symmetric Functions in Superspace

Year: 2024

Type: article

Abstract: 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.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12295

Authors: Diego Arcis, Camilo González, Sebastián Márquez

Institutions: University of La Serena, University of Concepción, Universidad Autónoma de Chile

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Agencia Nacional de Investigación y Desarrollo

Awards: OPERADORES DE CREACION PARA FUNCIONES SIMETRICAS, COMMUTATIVE AND NONCOMMUTATIVE SYMMETRIC FUNCTIONS IN SUPERSPACE.