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Splitting Algebras and Schubert Calculus
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2012 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 61, no 3, 1253-1312 p.Article in journal (Refereed) Published
Abstract [en]

We continue previous work on Schubert calculus of Grassmann schemes via splitting and factorization algebras. The aim of the project is to describe the intersection theory of flag schemes under very general conditions. In this part we extend, generalize, and refine the previous work. Among the main accomplishments of this article is the introduction of Schur determinants generalizing Schur polynomials. For the Schur determinants we obtain determinantal formulas, polarity formulas, and Gysin formulas in great generality. Our main tools are, as in our previous works, splitting and factorization algebras, residues of finite sets of Laurent series, and Gysin maps. The tools provide flexible techniques, useful in many parts of algebra, combinatorics, geometry and representation theory.

Place, publisher, year, edition, pages
2012. Vol. 61, no 3, 1253-1312 p.
Keyword [en]
splitting algebra, Schubert calculus, flag scheme, Grassmannian, Chow group, Giambellis formula, polarity formula, Gysin maps, Schubert conditions, determinantal formulas, Schur determinants
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-125797DOI: 10.1512/iumj.2012.61.4791ISI: 000321231000011Scopus ID: 2-s2.0-84880900539OAI: oai:DiVA.org:kth-125797DiVA: diva2:640663
Note

QC 20130814

Available from: 2013-08-14 Created: 2013-08-13 Last updated: 2017-12-06Bibliographically approved

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