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A determinantal formula for the exterior powers of the polynomial ring
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2007 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 56, no 2, 825-845 p.Article in journal (Refereed) Published
Abstract [en]

We present a very general, conceptually natural, explicit and computationally efficient Schubert calculus. It consists of two strongly interrelated parts, a structure theorem for an exterior power of the polynomial ring in one variable as a module over the ring of symmetric polynomials and a determinantal formula. Both parts are similar to corresponding results in algebra, combinatorics and geometry. To emphasize the connections with these fields we give several proofs of our main results, each proof illuminating the theory from a different algebraic, combinatorial, or geometric angle. The main application of our theory is to the Schubert calculus of Grassmann schemes, where it gives a natural homology and cohomology theory for the Grassmannians in a very general setting.

Place, publisher, year, edition, pages
2007. Vol. 56, no 2, 825-845 p.
Keyword [en]
determinantal formula, Schubert calculus, Gatto's formula, exterior, algebras, Giambelli's formula, Grassmann schemes, symmetric structures, symmetric functions, symmetrizing operators, divided difference, operators, intersection theory, universal splitting algebras, schubert calculus
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-16628DOI: 10.1512/iumj.2007.56.2937ISI: 000246462100012Scopus ID: 2-s2.0-34249785667OAI: oai:DiVA.org:kth-16628DiVA: diva2:334670
Note

QC 20100525

Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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