Quantum Integrability and Generalised Quantum Schubert Calculus

TL;DR

This paper connects quantum cohomology of Grassmannians with integrable systems, specifically the six-vertex model, providing new insights and conjectures in quantum K-theory.

Contribution

It introduces a novel link between Schubert calculus in quantum cohomology and quantum integrable systems, expanding understanding of equivariant K-theory.

Findings

Established a relation between Schubert calculus and the six-vertex model.

Provided a new perspective on equivariant K-theory.

Formulated a conjecture for quantum equivariant K-theory.

Abstract

We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric six-vertex model. Our approach offers a new perspective on already established and well-studied special cases, for example equivariant K-theory, and in addition allows us to formulate a conjecture on the so-far unknown case of quantum equivariant K-theory.