Bihamiltonian structures on compact hermitian symmetric spaces

In this thesis, we discuss a new approach to the problem of the diagonalization of the Nijenhuis tensor on compact hermitian symmetric spaces. Our attention is more focused on the hamiltonian forms rather than on the eigenvalues of the Nijenhuis tensor. This is motivated by the fact that the eigenvalues of N are only continuous functions and their derivatives have singularities. We describe these hamiltonian forms in terms of polynomials invariant with respect to a chain of subalgebra.