A Hopf algebraic approach to Schur function identities

TL;DR

This paper leverages the cocommutative Hopf algebra structure of symmetric functions to prove equalities among skew Schur functions, including some newly discovered identities.

Contribution

It introduces a Hopf algebraic method to establish skew Schur function identities, revealing new relations in symmetric function theory.

Findings

Proved equalities among skew Schur functions using Hopf algebra properties

Discovered new skew Schur function identities

Demonstrated the effectiveness of algebraic structures in combinatorial proofs

Abstract

Using cocommutativity of the Hopf algebra of symmetric functions, certain skew Schur functions are proved to be equal. Some of these skew Schur function identities are new.