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For $w$ a permutation, the associated (ordinary) Schubert polynomial $\mathfrak{S}_w(\textbf{x})$ is a multivariate polynomial that represents for the cohomology class of the Schubert variety $X_w$ in the flag variety. There are many references for this fact. See, e.g., this text by Manivel. One ...
In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by Lascoux & Schützenberger (1982) and are named after Hermann Schubert.
== Background ==
Lascoux (1995) described the history of Schubert polynomials.
The Schubert polynomials
S
w
{\displaystyle {\mathfrak {S}}_{w}}
are polynomials in the variables...
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