The ring of $\omega$-invariant symmetric functions in characteristic 2

Sebastian Ørsted

The ring of $\omega$-invariant symmetric functions in characteristic 2

Commutative Algebra 2026-05-14 v5

Authors: Sebastian Ørsted

Abstract

We provide a simple presentation by generators and relations of the ring of $\omega$ -invariant symmetric functions over the field $\mathbb{F}_{2}$ . Here, $\omega$ denotes the standard involution on the ring of symmetric functions, interchanging the elementary symmetric functions with the complete homogeneous symmetric functions. Along the way, we prove several important properties of this involution in the specific setting of characteristic 2.

Keywords

symmetric functions involution characteristic 2 generators and relations elementary symmetric functions complete homogeneous symmetric functions

Cite

@article{arxiv.2509.02177,
  title  = {The ring of $\omega$-invariant symmetric functions in characteristic 2},
  author = {Sebastian Ørsted},
  journal= {arXiv preprint arXiv:2509.02177},
  year   = {2026}
}

Comments

18 pages; added an extra chapter about the $\omega$-invariants in the $\mathbb{F}_2$-cohomology of the finite Grassmannian; a few minor corrections

The ring of $\omega$-invariant symmetric functions in characteristic 2

Abstract

Keywords

Cite

Comments

Related papers