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Complete integrability from Poisson-Nijenhuis structures on compact hermitian symmetric spaces
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2015 (English)Article in journal (Refereed) Submitted
Abstract [en]

We study a class of Poisson-Nijenhuis systems defined on compact hermitian symmetric spaces, where the Nijenhuis tensor is defined as the composition of Kirillov-Konstant-Souriau symplectic form with the so called Bruhat-Poisson structure. We determine its spectrum. In the case of Grassmannians the eigenvalues are the Gelfand-Tsetlin variables. We introduce the abelian algebra of collective hamiltonians defined by a chain of nested subalgebras and prove complete integrability. By construction, these models are integrable with respect to both Poisson structures. The eigenvalues of the Nijenhuis tensor are a choice of action variables. Our proof relies on an explicit formula for the contravariant connection defined on vector bundles that are Poisson with respect to the Bruhat-Poisson structure.

Place, publisher, year, edition, pages
National Category
Subatomic Physics
Research subject
Theoretical Physics
URN: urn:nbn:se:uu:diva-287825OAI: oai:DiVA.org:uu-287825DiVA: diva2:923504
Available from: 2016-04-26 Created: 2016-04-26 Last updated: 2016-04-26

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Qiu, Jian
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