Monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian

TL;DR

This paper analyzes the monodromy of the equivariant quantum differential equation for the cotangent bundle of a Grassmannian, linking it to equivariant K-theory and hypergeometric integrals, revealing polynomial structure in the monodromy matrices.

Contribution

It provides a new description of monodromy in terms of equivariant K-theory and hypergeometric integrals, with explicit polynomial entries in the monodromy matrices.

Findings

Monodromy matrices have Laurent polynomial entries with integer coefficients.

Solutions are identified with the equivariant K-theory algebra.

The approach uses hypergeometric integral representations.

Abstract

We describe the monodromy of the equivariant quantum differential equation of the cotangent bundle of a Grassmannian in terms of the equivariant K-theory algebra of the cotangent bundle. This description is based on the hypergeometric integral representations for solutions of the equivariant quantum differential equation. We identify the space of solutions with the space of the equivariant K-theory algebra of the cotangent bundle. In particular, we show that for any element of the monodromy group, all entries of its matrix in the standard basis of the equivariant K-theory algebra of the cotangent bundle are Laurent polynomials with integer coefficients in the exponentiated equivariant parameters.