Duke Mathematical Journal

Schubert polynomials and quiver formulas

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

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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.

Article information

Source
Duke Math. J. Volume 122, Number 1 (2004), 125-143.

Dates
First available in Project Euclid: 24 March 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1080137204

Digital Object Identifier
doi:10.1215/S0012-7094-04-12214-6

Mathematical Reviews number (MathSciNet)
MR2046809

Zentralblatt MATH identifier
02133135

Subjects
Primary: 05E15 14M15

Citation

Buch, Anders S.; Kresch, Andrew; Tamvakis, Harry; Yong, Alexander. Schubert polynomials and quiver formulas. Duke Math. J. 122 (2004), no. 1, 125--143. doi:10.1215/S0012-7094-04-12214-6. http://projecteuclid.org/euclid.dmj/1080137204.


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