1,491 research outputs found
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 skew
divided difference operators transform the Schubert polynomials into
polynomials with positive integer coefficients.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Notes on Schubert, Grothendieck and Key Polynomials
We introduce common generalization of (double) Schubert, Grothendieck,
Demazure, dual and stable Grothendieck polynomials, and Di
Francesco-Zinn-Justin polynomials. Our approach is based on the study of
algebraic and combinatorial properties of the reduced rectangular plactic
algebra and associated Cauchy kernels
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