Geodesic
Skew Divided Difference Operators and Schubert Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study an action of the skew divided difference operators on the Schubert polynomials and give an explicit formula for structural constants for the Schubert polynomials in terms of certain weighted paths in the Bruhat order on the symmetric group. We also prove that, under certain assumptions, the skew divided difference operators transform the Schubert polynomials into polynomials with positive integer coefficients.
Keywords: divided differences; nilCoxeter algebras; Schubert polynomials. 
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     author = {Anatol N. Kirillov},
     title = {Skew {Divided} {Difference} {Operators} and {Schubert} {Polynomials}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a71/}
}
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Anatol N. Kirillov. Skew Divided Difference Operators and Schubert Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a71/

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