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Article: Poisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/T

TitlePoisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/T
Authors
Issue Date1999
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim
Citation
Advances In Mathematics, 1999, v. 142 n. 2, p. 171-220 How to Cite?
AbstractWe characterize the harmonic forms on a flag manifoldK/Tdefined by Kostant in 1963 in terms of a Poisson structure. Namely, they are "Poisson harmonic" with respect to the so-called Bruhat Poisson structure onK/T. This enables us to give Poisson geometrical proofs of many of the special properties of these harmonic forms. In particular, we construct explicit representatives for the Schubert basis of theS1-equivariant cohomology ofK/T, where theS1-action is defined byρ. Using a simple argument in equivariant cohomology, we recover the connection between the Kostant harmonic forms and the Schubert calculus onK/Tthat was found by Kostant and Kumar in 1986. By using a family of symplectic structures onK/T, we also show that the Kostant harmonic forms are limits of the more familiar Hodge harmonic forms with respect to a family of Hermitian metrics onK/T. © 1999 Academic Press.
Persistent Identifierhttp://hdl.handle.net/10722/156080
ISSN
2015 Impact Factor: 1.405
2015 SCImago Journal Rankings: 3.261
References

 

DC FieldValueLanguage
dc.contributor.authorEvens, Sen_US
dc.contributor.authorLu, JHen_US
dc.date.accessioned2012-08-08T08:40:19Z-
dc.date.available2012-08-08T08:40:19Z-
dc.date.issued1999en_US
dc.identifier.citationAdvances In Mathematics, 1999, v. 142 n. 2, p. 171-220en_US
dc.identifier.issn0001-8708en_US
dc.identifier.urihttp://hdl.handle.net/10722/156080-
dc.description.abstractWe characterize the harmonic forms on a flag manifoldK/Tdefined by Kostant in 1963 in terms of a Poisson structure. Namely, they are "Poisson harmonic" with respect to the so-called Bruhat Poisson structure onK/T. This enables us to give Poisson geometrical proofs of many of the special properties of these harmonic forms. In particular, we construct explicit representatives for the Schubert basis of theS1-equivariant cohomology ofK/T, where theS1-action is defined byρ. Using a simple argument in equivariant cohomology, we recover the connection between the Kostant harmonic forms and the Schubert calculus onK/Tthat was found by Kostant and Kumar in 1986. By using a family of symplectic structures onK/T, we also show that the Kostant harmonic forms are limits of the more familiar Hodge harmonic forms with respect to a family of Hermitian metrics onK/T. © 1999 Academic Press.en_US
dc.languageengen_US
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/aimen_US
dc.relation.ispartofAdvances in Mathematicsen_US
dc.titlePoisson harmonic forms, Kostant harmonic forms, and the S1-equivariant cohomology of K/Ten_US
dc.typeArticleen_US
dc.identifier.emailLu, JH:jhluhku@hku.hken_US
dc.identifier.authorityLu, JH=rp00753en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0033602348en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0033602348&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume142en_US
dc.identifier.issue2en_US
dc.identifier.spage171en_US
dc.identifier.epage220en_US
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridEvens, S=6601953518en_US
dc.identifier.scopusauthoridLu, JH=35790078400en_US

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