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A Relation Between Symmetric Polynomials and the Algebra of Classes, Motivated by Equivariant Schubert Calculus
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry / [ed] Floystad, G; Johnsen, T; Knutsen, AL, Springer Berlin/Heidelberg, 2011, 89-97 p.Conference paper, Published paper (Refereed)
Abstract [en]

In previous work we developed a general formalism for equivariant Schubert calculus of grassmannians consisting of a basis theorem, a Pieri formula and a Giambelli formula. Part of the work consists in interpreting the results in a ring that can be considered as the formal generalized analog of localized equivariant cohomology of infinite grassmannians. Here we present an extract of the theory containing the essential features of this ring. In particular we emphasize the importance of the GKM condition. Our formalism and methods are influenced by the combinatorial formalism given by A. Knutson and T. Tao for equivariant cohomology of grassmannians, and of the use of factorial Schur polynomials in the work of L.C. Mihalcea.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 2011. 89-97 p.
Series
Abel Symposia, 6
Keyword [en]
Cohomology, Grassmannians
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-81941DOI: 10.1007/978-3-642-19492-4_7ISI: 000303079200007Scopus ID: 2-s2.0-84883628197ISBN: 978-3-642-19491-7 (print)OAI: oai:DiVA.org:kth-81941DiVA: diva2:497779
Conference
Abel Symposium on Combinatorial Aspects of Commutative Algebra and Algebraic Geometry June 1–4, 2009, Voss, Norway,June 01-04, 2009
Note
QC 20120425Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-08-22Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • modern-language-association-8th-edition
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  • nn-NB
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