Complete integrability from Poisson-Nijenhuis structures on compact hermitian symmetric spaces

Authors: Francesco Bonechi, Jian Qiu, Marco Tarlini Preprint number: UUITP-08/15 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-Cetlin variables. We introduce the abelian algebra