Quantum cohomology of Grassmannians

TL;DR

This paper provides elementary proofs of key theorems in the quantum cohomology of Grassmannians, including formulas, algorithms, and presentations, clarifying foundational aspects of the subject.

Contribution

It offers simplified, elementary proofs of major results in quantum cohomology of Grassmannians, making the theory more accessible.

Findings

Elementary proofs of quantum Giambelli and Pieri formulas

Validation of the rim-hook algorithm and Siebert-Tian presentation

Clarification of Fulton-Woodward's minimal q-power theorem

Abstract

We give elementary proofs of the main theorems about (small) quantum cohomology of Grassmannians, including the quantum Giambelli and quantum Pieri formulas, the rim-hook algorithm, Siebert and Tian's presentation, and a recent theorem of Fulton and Woodward about the minimal q-power which appears in a product of two Schubert classes.