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Schubert polynomials and quiver formulas. (English) Zbl 1072.14067
A. Skovsted Buch and W. Fulton [Invent. Math. 135, No. 3, 665–687 (1999; Zbl 0942.14027)] gave a formula for a general kind of degeneracy locus associated to an oriented Type A quiver. This formula involves Schur determinants and the quiver coefficients which generalize the classical Littlewood-Richardson coefficients. In the paper under review, the authors give a positive combinatorial formula for the quiver coefficients when the rank conditions defining the degeneracy locus are given by a permutation. As applications, one obtains new expansions for Fulton’s universal Schubert polynomials, Schubert polynomials of Lascoux-Schützenberger, and explicit Giambelli formulas in the classical and quantum cohomology ring of any partial flag variety.

MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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