# On the coproduct in affine Schubert calculus

## TL;DR

This paper provides positive formulas for the coproduct of affine Schubert classes in cohomology and K-theory, connecting affine Stanley and finite Schubert classes, and demonstrates monomial positivity of affine Schubert polynomials.

## Contribution

It introduces explicit positive formulas for coproducts in affine Schubert calculus, linking affine Stanley classes with finite Schubert classes in cohomology and K-theory.

## Key findings

- Positive formulas for coproducts in affine Schubert calculus
- Monomial positivity of affine Schubert polynomials
- Connection between affine Stanley classes and finite Schubert classes

## Abstract

The cohomology of the affine flag variety of a complex reductive group is a comodule over the cohomology of the affine Grassmannian. We give positive formulae for the coproduct of an affine Schubert class in terms of affine Stanley classes and finite Schubert classes, in (torus-equivariant) cohomology and K-theory. As an application, we deduce monomial positivity for the affine Schubert polynomials of the second author.