On equivariant quantum Schubert calculus for G/P

TL;DR

This paper develops a new algebraic framework for torus-equivariant quantum cohomology of flag varieties, extending previous results and providing explicit rules for calculations in equivariant quantum Schubert calculus.

Contribution

It introduces a Z^2-filtered algebraic structure and a quantum to classical principle, generalizing earlier work and deriving an equivariant quantum Pieri rule for partial flag varieties of Lie type A.

Findings

Established a Z^2-filtered algebraic structure.

Proved a quantum to classical principle in the setting.

Derived an equivariant quantum Pieri rule for Lie type A.

Abstract

We show a Z^2-filtered algebraic structure and a "quantum to classical" principle on the torus-equivariant quantum cohomology of a complete flag variety of general Lie type, generalizing earlier works of Leung and the second author. We also provide various applications on equivariant quantum Schubert calculus, including an equivariant quantum Pieri rule for any partial flag variety of Lie type A.