A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus

In previous work we developed a general formalism for equivariant Schubert calculus of grassmannians consisting of a basis theorem, a Pieri formula and a Giambelli formula. Part of the work consists in interpreting the results in a ring that can be considered as the formal generalized analog of localized equivariant cohomology of infinite grassmannians. Here we present an extract of the theory containing the essential features of this ring. In particular we emphasize the importance of the GKM condition. Our formalism and methods are influenced by the combinatorial formalism given by A. Knutson and T. Tao for equivariant cohomology of grassmannians, and of the use of factorial Schur polynomials in the work of L.C. Mihalcea.