Skew Schubert Functions and the Pieri Formula for Flag Manifolds

  title={Skew Schubert Functions and the Pieri Formula for Flag Manifolds},
  author={Nantel Bergeron and Frank Sottile},
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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Publications referenced by this paper.
Showing 1-10 of 33 references

On the number of reduced decompositions of elements of Coxeter groups

  • R. Stanley
  • Europ. J. Combin., 5
  • 1984
Highly Influential
17 Excerpts

Schubert polynomials

  • N. Bergeron, F. Sottile
  • the Bruhat order, and the geometry of flag…
  • 1998
Highly Influential
8 Excerpts

Le monöıde plaxique

  • A. Lascoux, M.-P. Schützenberger
  • Non-Commutative Structures in Algebra and…
  • 1981
Highly Influential
6 Excerpts


  • D. Knuth
  • matrices and generalized Young tableaux, Pacific…
  • 1970
Highly Influential
5 Excerpts

MR 2000 d : 05127 [ 4 ] , A monoid for the Grassmannian Bruhat order

  • I. N. Bernstein, I. M. Gelfand, S. I. Gelfand
  • Europ . J . Combinatorics
  • 1999

Fonctions symétriques

  • L. Manivel
  • polynômes de Schubert et lieux de dégénérescence…
  • 1998
3 Excerpts

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