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Schubert polynomials and quiver formulas


Buch, A; Kresch, A; Tamvakis, H; Yong, A (2004). Schubert polynomials and quiver formulas. Duke Mathematical Journal, 122(1):125-143.

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.

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.

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16 citations in Web of Science®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:quiver coefficients
Language:English
Date:2004
Deposited On:29 Nov 2010 16:26
Last Modified:05 Apr 2016 13:24
Publisher:Duke University Press
ISSN:0012-7094
Additional Information:2004 © Duke University Press
Publisher DOI:https://doi.org/10.1215/S0012-7094-04-12214-6
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2046809
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1072.14067
Permanent URL: https://doi.org/10.5167/uzh-21772

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