Skew Schubert Functions and the Pieri Formula for Flag Manifolds

@inproceedings{Bergeron1997SkewSF,
  title={Skew Schubert Functions and the Pieri Formula for Flag Manifolds},
  author={Nantel Bergeron and Frank Sottile},
  year={1997}
}
We show the equivalence of the Pieri formula for flag manifolds with certain identities among the structure constants for the Schubert basis of the polynomial ring. This gives new proofs of both the Pieri formula and of these identities. A key step is the association of a symmetric function to a finite poset with labeled Hasse diagram satisfying a symmetry condition. This gives a unified definition of skew Schur functions, Stanley symmetric functions, and skew Schubert functions (defined here… CONTINUE READING
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