Equivariant quantum Schubert polynomials

TL;DR

This paper develops an equivariant quantum Giambelli formula for partial flag varieties using universal double Schubert polynomials, providing new proofs and positivity results in equivariant quantum Schubert calculus.

Contribution

It introduces a novel equivariant quantum Giambelli formula and new proofs for the structure of the equivariant quantum cohomology ring.

Findings

Established an equivariant quantum Giambelli formula.

Provided new proofs of the presentation of the equivariant quantum cohomology ring.

Proved Graham-positivity of structure constants.

Abstract

We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus.