Skew divided difference operators and Schubert polynomials

Details Skew divided difference operators and Schubert polynomials Skew divided difference operators and Schubert polynomials

1997-12-25

arxiv.org/abs/q-alg/9712053v1

Mathematics

Quantum Algebra

PlainTeX, 15 pages

Scientific paper

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 Schubert polynomials into polynomials with positive integer coefficients.

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