A BI-HAMILTONIAN SYSTEM ON THE GRASSMANNIAN

作者：Bonechi F^*; Qiu J; Tarlini M^*

来源：Theoretical and Mathematical Physics, 2016, 189(1): 1401-1410.

DOI：10.1134/S0040577916100019

• symplectic geometry
• integrable system
• Poisson-Nijenhuis geometry
• Poisson manifold quantization
• symplectic groupoid

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.

• 出版日期2016-10