Equivariant Cohomology of Weighted Grassmannians and Weighted Schubert Classes

In this paper, we study the Tw-equivariant cohomology of the weighted Grassmannians wGr(d,n) introduced by Corti-Reid [4], where Tw is the n-dimensional torus that naturally acts on wGr(d,n). We introduce the equivariant weighted Schubert classes and, after we show that they form a basis of the equivariant cohomology, we give an explicit formula for the structure constants with respect to this Schubert basis. We also find a linearly independent subset {wu1,...,wun-1} of Lie(Tw)* such that those structure constants are polynomials in wui's with nonnegative coefficients, up to a permutation on the weights.