We describe the torus-equivariant cohomology ring of isotropic Grassmannians
by using a localization map to the torus fixed points. We present two types of
formulas for equivariant Schubert classes of these homogeneous spaces. The
first formula involves combinatorial objects which we call ``excited Young
diagrams'' and the second one is written in terms of factorial Schur Q- or
P-functions. As an application, we give a Giambelli-type formula for the
equivariant Schubert classes. We also give combinatorial and Pfaffian formulas
for the multiplicity of a singular point in a Schubert variety.Comment: 29 page