Quantum multiplication through equivariant Schubert calculus

In this note, we rederive quantum Pieri’s formula and the rim hook algorithm in quantum Schubert calculus by studying multiplication in the equivariant cohomology ring of Grassmannians with respect to equivariant Schubert classes which are characteristic classes. We also extend this idea in studying equivariant quantum Schubert calculus, and obtain the equivariant quantum Giambelli’s and Pieri’s formulae in terms of characteristic classes, with the former formula shown to be free of quantum deformation.