Skew Schubert polynomials |
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| Authors: | Cristian Lenart Frank Sottile |
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| Affiliation: | Department of Mathematics and Statistics, State University of New York at Albany, Albany, New York 12222 ; Department of Mathematics, University of Massachusetts, Amherst, Massachusetts 01003 |
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| Abstract: | We define skew Schubert polynomials to be normal form (polynomial) representatives of certain classes in the cohomology of a flag manifold. We show that this definition extends a recent construction of Schubert polynomials due to Bergeron and Sottile in terms of certain increasing labeled chains in Bruhat order of the symmetric group. These skew Schubert polynomials expand in the basis of Schubert polynomials with nonnegative integer coefficients that are precisely the structure constants of the cohomology of the complex flag variety with respect to its basis of Schubert classes. We rederive the construction of Bergeron and Sottile in a purely combinatorial way, relating it to the construction of Schubert polynomials in terms of rc-graphs. |
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| Keywords: | Schubert polynomial Bruhat order Littlewood-Richardson coefficient |
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