Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 072, 14 pages      arXiv:0705.4546      http://dx.doi.org/10.3842/SIGMA.2007.072
Contribution to the Vadim Kuznetsov Memorial Issue

Skew Divided Difference Operators and Schubert Polynomials

Anatol N. Kirillov
Research Institute of Mathematical Sciences (RIMS), Sakyo-ku, Kyoto 606-8502, Japan

Received May 01, 2007; Published online May 31, 2007

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.

Key words: divided differences; nilCoxeter algebras; Schubert polynomials.

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