Hopf algebra structure of symmetric and quasisymmetric functions in superspace
Combinatorics
2019-07-24 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1907.09975,
title = {Hopf algebra structure of symmetric and quasisymmetric functions in superspace},
author = {Susanna Fishel and Luc Lapointe and Maria Elena Pinto},
journal= {arXiv preprint arXiv:1907.09975},
year = {2019}
}