# Schubert polynomials, theta and eta polynomials, and Weyl group invariants

## TL;DR

This paper explores the connections between Schubert polynomials, theta and eta polynomials, and Weyl group invariants, providing generators for kernels related to symplectic and orthogonal flag manifolds' cohomology.

## Contribution

It establishes a link between different polynomial families and Weyl group invariants, identifying generators for kernels in cohomology ring mappings.

## Key findings

- Identifies generators for the kernel of the natural map from Schubert polynomials to cohomology rings.
- Clarifies the relationship between Schubert, theta, and eta polynomials within Weyl group invariants.
- Provides algebraic tools for understanding cohomology of symplectic and orthogonal flag manifolds.

## Abstract

We examine the relationship between the (double) Schubert polynomials of Billey-Haiman and Ikeda-Mihalcea-Naruse and the (double) theta and eta polynomials of Buch-Kresch-Tamvakis and Wilson from the perspective of Weyl group invariants. We obtain generators for the kernel of the natural map from the corresponding ring of Schubert polynomials to the (equivariant) cohomology ring of symplectic and orthogonal flag manifolds.