Minimum quantum degrees with Maya diagrams

TL;DR

This paper introduces a combinatorial approach using Maya diagrams to determine the minimal quantum degrees in the quantum cohomology of partial flags, providing a new proof of their uniqueness and offering visual calculation rules.

Contribution

It refines existing criteria for minimal quantum degrees using Maya diagrams and provides a combinatorial proof of their uniqueness in partial flag varieties.

Findings

Maya diagrams effectively identify minimal quantum degrees.

The approach confirms the uniqueness of minimal quantum degrees.

Visual rules facilitate precise combinatorial calculations.

Abstract

We use Maya diagrams to refine the criterion by Fulton and Woodward for the smallest powers of the quantum parameter $q$ that occur in a product of Schubert classes in the (small) quantum cohomology of partial flags. Our approach using Maya diagrams yields a combinatorial proof that the minimal quantum degrees are unique for partial flags. Furthermore, visual combinatorial rules are given to perform precise calculations.