Skew Schubert functions and the Pieri formula for flag manifolds

Details Skew Schubert functions and the Pieri formula for flag manifolds Skew Schubert functions and the Pieri formula for flag manifolds

1997-09-30

arxiv.org/abs/alg-geom/9709034v1

Trans. Amer. Math. Soc., 354 No. 2, (2002), 651-673.

Mathematics

Algebraic Geometry

24 pages, LaTeX 2e, with epsf.sty

Scientific paper

We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving 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 function, and skew Schubert functions (defined here). We also use algebraic geometry to show the coefficient of a monomial in a Schubert polynomial counts certain chains in the Bruhat order, obtaining a new combinatorial construction of Schubert polynomials.

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