Quantum Generalization of the Horn Conjecture

TL;DR

This paper proves a quantum analogue of the Horn conjecture and saturation conjecture, establishing new transversality results in quantum Schubert calculus and determining minimal powers of q in quantum products.

Contribution

It introduces a quantum generalization of the Horn conjecture, extending classical results to the quantum setting and providing new algebraic and geometric insights.

Findings

Proves a quantum analogue of the Horn conjecture.

Establishes transversality in quantum Schubert calculus.

Determines the smallest power of q in quantum products.

Abstract

We prove a theorem which implies a quantum (multiplicative) analogue of the Horn conjecture, and also of the saturation conjecture. We obtain transversality statements for quantum schubert calculus in any characteristic and also determine the smallest power of q in an arbitrary (small quantum) product of Schubert varieties in a Grassmannian.