  In this paper, we introduce a family of symmetric polynomials by specializing
the factorial Schur polynomials. These polynomials represent the weighted
Schubert classes of the cohomology of the weighted Grassmannian introduced by
Corti-Reid, and we regard these polynomials as analogue of the Schur
polynomials. We show that those twisted Schur polynomials are the characters of
certain representations. Thus we give an interpretation of the Schubert
structure constants of the weighted Grassmannians as the (rational)
multiplicities of tensor products of the representations. Furthermore, we
derive two types of determinantal formulas for the weighted Schubert classes,
in terms of special weighted Schubert classes, and also in terms of Chern
classes of tautological orbi-bundles.
