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Symmetry, Integrability and Geometry: Methods and Applications, 2007, Volume 3, 072, 14 pp.
DOI: https://doi.org/10.3842/SIGMA.2007.072 (Mi sigma198) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Skew Divided Difference Operators and Schubert Polynomials

Anatol N. Kirillov

Research Institute of Mathematical Sciences (RIMS), Sakyo-ku, Kyoto 606-8502, Japan
Full-text PDF (252 kB) Citations (4)
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DOI: https://doi.org/10.3842/SIGMA.2007.072
Abstract: 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.
Received: May 1, 2007; Published online May 31, 2007
Bibliographic databases:
Document Type: Article
MSC: 05E15; 05E05
Language: English
Citation: Anatol N. Kirillov, “Skew Divided Difference Operators and Schubert Polynomials”, SIGMA, 3 (2007), 072, 14 pp.
Citation in format AMSBIB
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\by Anatol N.~Kirillov
\paper Skew Divided Difference Operators and Schubert Polynomials
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\vol 3
\papernumber 072
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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