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Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21955

Kresch, A; Tamvakis, H (2002). Double Schubert polynomials and degeneracy loci for the classical groups. Annales de l'institut Fourier, 52(6):1681-1727.

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Abstract

We propose a theory of double Schubert polynomials $P_w(X,Y)$ for the Lie types $B$, $C$, $D$ which naturally extends the family of Lascoux and Schützenberger in type $A$. These polynomials satisfy positivity, orthogonality and stability properties, and represent the classes of Schubert varieties and degeneracy loci of vector bundles. When $w$ is a maximal Grassmannian element of the Weyl group, $P_w(X,Y)$ can be expressed in terms of Schur-type determinants and Pfaffians, in analogy with the type $A$ formula of Kempf and Laksov. An example, motivated by quantum cohomology, shows there are no Chern class formulas for degeneracy loci of "isotropic morphisms" of bundles.

Citations

14 citations in Web of Science®
15 citations in Scopus®
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26 downloads since deposited on 18 Feb 2010
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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:degeneracy loci, Schubert polynomials
Language:English
Date:2002
Deposited On:18 Feb 2010 11:26
Last Modified:05 Apr 2016 13:25
Publisher:Association des Annales de l'Institut Fourier
ISSN:0373-0956
Additional Information:© Association des Annales de l'institut Fourier, 2002, touts droits réservés
Official URL:http://aif.cedram.org/item?id=AIF_2002__52_6_1681_0
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1952528
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1059.14063

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