# Euler characteristics of cominuscule quantum K-theory

## TL;DR

This paper establishes a fundamental identity in cominuscule quantum K-theory linking Schubert varieties and rational curves, showing the sum of structure constants equals one and extending the Euler characteristic map to a ring homomorphism.

## Contribution

It introduces a new identity connecting Schubert varieties and rational curves in quantum K-theory, and extends the sheaf Euler characteristic map to a ring homomorphism.

## Key findings

- Sum of structure constants for Schubert class products equals one
- Sheaf Euler characteristic map extends to quantum K-theory ring
- Identifies minimal degree of rational curves connecting Schubert varieties

## Abstract

We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce that the sum of the structure constants associated to any product of Schubert classes is equal to one. Equivalently, the sheaf Euler characteristic map extends to a ring homomorphism defined on the quantum K-theory ring.