Equivariant Schubert calculus

Abstract

We describe T-equivariant Schubert calculus on G(k, n), T being an n-dimensional torus, through derivations on the exterior algebra of a free A-module of rank n, where A is the T-equivariant cohomology of a point. In particular, T-equivariant Pieri’s formulas will be determined, answering a question raised by Lakshmibai, Raghavan and Sankaran (Equivariant Giambelli and determinantal restriction formulas for the Grassmannian, Pure Appl. Math. Quart. 2 (2006), 699–717).