Schubert polynomials and quiver formulas

Anders S. Buch, Andrew Kresch, Harry Tamvakis, Alexander Yong

Research output: Contribution to journalReview articlepeer-review

22 Scopus citations

Abstract

Fulton's universal Schubert polynomials [F3] represent degeneracy loci for morphisms of vector bundles with rank conditions coming from a permutation. The quiver formula of Buch and Fulton [BF] expresses these polynomials as an integer linear combination of products of Schur determinants. We present a positive, nonrecursive combinatorial formula for the coefficients. Our result is applied to obtain new expansions for the Schubert polynomials of Lascoux and Schützenberger [LS1] and explicit Giambelli formulas in the classical and quantum cohomology ring of any partial flag variety.

Original languageEnglish (US)
Pages (from-to)125-143
Number of pages19
JournalDuke Mathematical Journal
Volume122
Issue number1
DOIs
StatePublished - Mar 15 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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