Skew Schubert functions and the Pieri formula for flag manifolds

Abstract

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.

24 pages, LaTeX 2e, with epsf.sty

Cited by in corpus (7)

• Schubert polynomials, the Bruhat order, and the geometry of flag manifolds
• The peak algebra and the descent algebras of types B and D
• Skew quasisymmetric Schur functions and noncommutative Schur functions
• Multiplicative structures of the immaculate basis of non-commutative symmetric functions
• Peaks Sets of Classical Coxeter Groups
• Fomin-Greene monoids and Pieri operations
• A Molev-Sagan type formula for double Schubert polynomials