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Grothendieck polynomials and quiver formulas


Buch, A; Kresch, A; Tamvakis, H; Yong, A (2005). Grothendieck polynomials and quiver formulas. American Journal of Mathematics, 127(3):551-567.

Abstract

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have alternating signs. Our result is applied to obtain new expansions for the Grothendieck polynomials of Lascoux and Schützenberger.

Fulton's universal Schubert polynomials give cohomology formulas for a class of degeneracy loci, which generalize Schubert varieties. The K-theoretic quiver formula of Buch expresses the structure sheaves of these loci as integral linear combinations of products of stable Grothendieck polynomials. We prove an explicit combinatorial formula for the coefficients, which shows that they have alternating signs. Our result is applied to obtain new expansions for the Grothendieck polynomials of Lascoux and Schützenberger.

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4 citations in Web of Science®
6 citations in Scopus®
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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
Language:English
Date:2005
Deposited On:08 Feb 2010 14:26
Last Modified:05 Apr 2016 13:24
Publisher:The Johns Hopkins University Press
ISSN:0002-9327
Publisher DOI:10.1353/ajm.2005.0017
Permanent URL: http://doi.org/10.5167/uzh-21683

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