In previous work we have developed a general formalism for Schubert calculus. Here we show how this theory can be adapted to give a formalism for equivariant Schubert calculus consisting of a basis theorem, a Pieri formula and a Giambelli formula. Our theory specializes to a formalism for equivariant cohomology of grassmannians. We interpret the results in a ring that can be considered as the formal generalized analog of localized equivariant cohomology of infinite grassmannians.
"A formalism for equivariant Schubert calculus." Algebra Number Theory 3 (6) 711 - 727, 2009. https://doi.org/10.2140/ant.2009.3.711