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A bi-Hamiltonian system on the Grassmannian
Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
Natl Inst Nucl Phys, Sez Firenze, Florence, Italy..
2016 (English)In: Theoretical and mathematical physics, ISSN 0040-5779, E-ISSN 1573-9333, Vol. 189, no 1, 1401-1410 p.Article in journal (Refereed) Published
Abstract [en]

Considering the recent result that the Poisson-Nijenhuis geometry corresponds to the quantization of the symplectic groupoid integrating a Poisson manifold, we discuss the Poisson-Nijenhuis structure on the Grassmannian defined by the compatible Kirillov-Kostant-Souriau and Bruhat-Poisson structures. The eigenvalues of the Nijenhuis tensor are Gelfand-Tsetlin variables, which, as was proved, are also in involution with respect to the Bruhat-Poisson structure. Moreover, we show that the Stiefel bundle on the Grassmannian admits a bi-Hamiltonian structure.

Place, publisher, year, edition, pages
2016. Vol. 189, no 1, 1401-1410 p.
Keyword [en]
symplectic geometry, integrable system, Poisson-Nijenhuis geometry, Poisson manifold quantization, symplectic groupoid
National Category
Physical Sciences Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-308943DOI: 10.1134/S0040577916100019ISI: 000386870200001OAI: oai:DiVA.org:uu-308943DiVA: diva2:1052946
Available from: 2016-12-07 Created: 2016-12-01 Last updated: 2017-02-20Bibliographically approved

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