Bases for Quotients of Symmetric Polynomials

TL;DR

This paper introduces new bases for symmetric polynomials and demonstrates that certain Schur polynomials form bases for quotients related to Grassmannian cohomology, offering new proofs and generalizations.

Contribution

It constructs novel bases for symmetric polynomials and shows their application to quotients relevant to Grassmannian cohomology, extending previous results.

Findings

Schur polynomials form bases for specific quotient rings

New bases for symmetric polynomials are constructed

Provides an alternative proof of Grinberg's result

Abstract

We create several families of bases for the symmetric polynomials. From these bases we prove that certain Schur symmetric polynomials form a basis for quotients of symmetric polynomials that generalize the cohomology and the quantum cohomology of the Grassmannian. Our work also provides an alternative proof of a result due to Grinberg.