Hopf algebra structure of symmetric and quasisymmetric functions in superspace

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:166

Article

Fishel, Susanna¹  Lapointe, Luc²  Elena Pinto, Maria² 

[1] Arizona State Univ, Sch Math & Stat Sci, POB 871804, Tempe, AZ 85287 USA

[2] Univ Talca, Inst Matemat & Fis, Casilla 747, Talca, Chile

关键词: Symmetric functions;    Quasisymmetric functions;    Hopf algebras;    Superspace;   

DOI  :  10.1016/j.jcta.2019.02.016

来源: Elsevier

【 摘 要 】

We show that the ring of symmetric functions in superspace is a cocommutative and self-dual Hopf algebra. We provide formulas for the action of the coproduct and the antipode on various bases of that ring. We introduce the ring sQSym of quasisymmetric functions in superspace and show that it is a Hopf algebra. We give explicitly the product, coproduct and antipode on the basis of monomial quasisymmetric functions in superspace. We prove that the Hopf dual of sQSym, the ring sNSym of noncommutative symmetric functions in superspace, has a multiplicative basis dual to the monomial quasisymmetric functions in superspace. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free