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Schubert calculus and equivariant cohomology of grassmannians
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2008 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 217, no 4, 1869-1888 p.Article in journal (Refereed) Published
Abstract [en]

We give a description of equivariant cohomology of grassmannians that places the theory into a general framework for cohomology theories of grassmannians. As a result we obtain a formalism for equivariant cohomology where the basic results of equivariant Schubert calculus, the basis theorem, Pieri's formula and Giambelli's formula can be obtained from the corresponding results of the general framework by a change of basis. In order to show that our formalism reflects the geometry of grassmannians we relate our theory to the treatment of equivariant cohomology of grassmannians by A. Knutson and T. Tao.

Place, publisher, year, edition, pages
2008. Vol. 217, no 4, 1869-1888 p.
Keyword [en]
equivariant cohomology, Schubert calculus, grassmannians, quantum, cohomology, factorization, quantum cohomology, flag manifolds, toda-lattices, formula, ring
Identifiers
URN: urn:nbn:se:kth:diva-17346DOI: 10.1016/j.aim.2007.09.014ISI: 000253508400012Scopus ID: 2-s2.0-38149024866OAI: oai:DiVA.org:kth-17346DiVA: diva2:335390
Note
QC 20100525Available from: 2010-08-05 Created: 2010-08-05 Last updated: 2017-12-12Bibliographically approved

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