Quasi-symmetric and non-commutative affine Schur functions

TL;DR

This paper introduces dual Hopf algebras that unify k-Schur functions with quasi-symmetric Schur functions, providing new dual bases with notable properties.

Contribution

It presents a novel construction of dual Hopf algebras combining k-Schur and quasi-symmetric Schur functions, advancing algebraic combinatorics.

Findings

Construction of dual bases with remarkable properties

Unification of k-Schur and quasi-symmetric Schur function theories

New algebraic structures for symmetric functions

Abstract

We introduce dual Hopf algebras which simultaneously combine the concepts of the k-Schur function theory with the quasi-symmetric Schur function theory. We construct dual basis of these Hopf algebras with remarkable properties.