Skew Divided Difference Operators and Schubert Polynomials

Details Skew Divided Difference Operators and Schubert Polynomials Skew Divided Difference Operators and Schubert Polynomials

2007-05-31

arxiv.org/abs/0705.4546v1

SIGMA 3 (2007), 072, 14 pages

Mathematics

Quantum Algebra

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.072

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.

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