# Minuscule Schubert calculus and the geometric Satake correspondence

## TL;DR

This paper connects Schubert calculus with the geometric Satake correspondence, providing new proofs of classical formulas and a simplified derivation of the rim-hook rule for quantum cohomology of Grassmannians.

## Contribution

It establishes a novel relationship between Schubert calculus and the geometric Satake correspondence, offering new proofs and computational rules.

## Key findings

- New proofs of equivariant Giambelli formulas for Grassmannians
- Simplified derivation of the rim-hook rule in quantum cohomology
- Established connection between Schubert calculus and geometric Satake correspondence

## Abstract

We describe a relationship between work of Laksov, Gatto, and their collaborators on realizations of (generalized) Schubert calculus of Grassmannians, and the geometric Satake correspondence of Lusztig, Ginzburg, and Mirkovi\'c and Vilonen. Along the way we obtain new proofs of equivariant Giambelli formulas for the ordinary and orthogonal Grassmannians, as well as a simple derivation of the "rim-hook" rule for computing in the equivariant quantum cohomology of the Grassmannian.