Equivariant Giambelli and determinantal restriction formulas for the   Grassmannian
  The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in the torus equivariant integral cohomology ring of the Grassmannian. As a corollary, we obtain an equivariant version of the Giambelli formula. 
V. Lakshmibai, K. N. Raghavan, P. Sankaran