On equivariant quantum Schubert calculus for G/PG/P

We show a Z2Z2-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 partial flag variety Fℓn1,⋯,nk;n+1Fℓn1,⋯,nk;n+1 of Lie type A.