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Mosc. Math. J., 2016, Volume 16, Number 1, Pages 125–177 (Mi mmj596)  

This article is cited in 4 scientific papers (total in 4 papers)

Giambelli and degeneracy locus formulas for classical $G/P$ spaces

Harry Tamvakis

University of Maryland, Department of Mathematics, 1301 Mathematics Building, College Park, MD 20742, USA

Abstract: Let $G$ be a classical complex Lie group, $P$ any parabolic subgroup of $G$, and $X=G/P$ the corresponding homogeneous space, which parametrizes (isotropic) partial flags of subspaces of a fixed vector space. In the mid 1990s, Fulton, Pragacz, and Ratajski asked for global formulas which express the cohomology classes of the universal Schubert varieties in flag bundles – when the space $X$ varies in an algebraic family – in terms of the Chern classes of the vector bundles involved in their definition. This has applications to the theory of degeneracy loci of vector bundles and is closely related to the Giambelli problem for the torus-equivariant cohomology ring of $X$. In this article, we explain the answer to these questions which was obtained in 2009 by the author, in terms of combinatorial data coming from the Weyl group.

Key words and phrases: Schubert calculus, Giambelli formulas, Schubert polynomials, degeneracy loci, equivariant cohomology.

Funding Agency Grant Number
National Science Foundation DMS-0901341
DMS-1303352
The author was supported in part by NSF Grants DMS-0901341 and DMS-1303352.


DOI: https://doi.org/10.17323/1609-4514-2016-16-1-125-177

Full text: http://www.mathjournals.org/.../2016-016-001-005.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 14M15; Secondary 05E15, 14M17, 14N15, 05E05
Received: January 30, 2014; in revised form August 7, 2015
Language:

Citation: Harry Tamvakis, “Giambelli and degeneracy locus formulas for classical $G/P$ spaces”, Mosc. Math. J., 16:1 (2016), 125–177

Citation in format AMSBIB
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\by Harry~Tamvakis
\paper Giambelli and degeneracy locus formulas for classical $G/P$ spaces
\jour Mosc. Math.~J.
\yr 2016
\vol 16
\issue 1
\pages 125--177
\mathnet{http://mi.mathnet.ru/mmj596}
\crossref{https://doi.org/10.17323/1609-4514-2016-16-1-125-177}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3470578}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000386360200005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tamvakis H., “Double Eta Polynomials and Equivariant Giambelli Formulas”, J. Lond. Math. Soc.-Second Ser., 94:1 (2016), 209–229  crossref  mathscinet  zmath  isi
    2. Tamvakis H., Wilson E., “Double Theta Polynomials and Equivariant Giambelli Formulas”, Math. Proc. Camb. Philos. Soc., 160:2 (2016), 353–377  crossref  mathscinet  zmath  isi  scopus
    3. D. Anderson, W. Fulton, “Chern class formulas for classical-type degeneracy loci”, Compos. Math., 154:8 (2018), 1746–1774  crossref  mathscinet  zmath  isi  scopus
    4. H. Tamvakis, “Schubert polynomials and degeneracy locus formulas”, Schubert Varieties, Equivariant Cohomology and Characteristic Classes–IMPANGA 15, EMS Ser. Congr. Rep., eds. J. Buczynski, M. Michalek, E. Postinghel, Eur. Math. Soc., Zürich, 2018, 261–314  mathscinet  zmath  isi
  • Moscow Mathematical Journal
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