Geodesic
Schur polynomials and weighted Grassmannians
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 875-892.

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In this paper, we introduce a family of symmetric polynomials by specializing the factorial Schur polynomials. We show that it represents the weighted Schubert classes of the cohomology of the weighted Grassmannian introduced by Corti-Reid, and we regard it as an analogue of the Schur polynomials. Furthermore, we prove that these polynomials are the characters of certain representations, and hence, we give an interpretation of the Schubert structure constants of the weighted Grassmannians as the (rational) multiplicities of the tensor products of the representations. We also derive two determinantal formulas for the weighted Schubert classes: One is in terms of the special weighted Schubert classes, and the other is in terms of the Chern classes of the tautological orbi-bundles.
Classification : 05E05, 05E15, 05E10, 57R18, 14N15
Keywords: Schur polynomial, weighted Grassmannian, orbifold, Schubert calculus, representation 
@article{JAC_2015__42_3_a0,
     author = {Abe, Hiraku and Matsumura, Tomoo},
     title = {Schur polynomials and weighted {Grassmannians}},
     journal = {Journal of Algebraic Combinatorics},
     pages = {875--892},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a0/}
}
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Abe, Hiraku; Matsumura, Tomoo. Schur polynomials and weighted Grassmannians. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 875-892. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a0/