Skew Divided Difference Operators and Schubert Polynomials

Skew Divided Difference Operators and Schubert Polynomials

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...

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Bibliographic Details
Main Author: Anatol N. Kirillov
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2007-05-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
divided differences
nilCoxeter algebras
Schubert polynomials
Online Access:http://www.emis.de/journals/SIGMA/2007/072/
Description
Summary: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.
ISSN:1815-0659

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