Quantum integrable model for the quantum cohomology/K-theory of flag varieties and the double $\beta$-Grothendieck polynomials

TL;DR

This paper introduces a quantum integrable model that captures the algebraic structures of quantum cohomology and K-theory of flag varieties, linking Bethe ansatz states to double β-Grothendieck polynomials.

Contribution

It presents a novel quantum integrable system that encodes ring relations of quantum cohomology and K-theory, connecting integrable models with algebraic geometry.

Findings

The integrable system generalizes the asymmetric five vertex spin chain.

Bethe ansatz states generate double β-Grothendieck polynomials.

The model encodes the ring relations of quantum cohomology and K-theory.

Abstract

A GL$(n)$ quantum integrable system generalizing the asymmetric five vertex spin chain is shown to encode the ring relations of the equivariant quantum cohomology and equivariant quantum K-theory ring of flag varieties. We also show that the Bethe ansatz states of this system generate the double $\beta$-Grothendieck polynomials.