he c .Neumann's system is an example of integrable systems with n degrees of freedom. In fact, this system describes a moving particle on the sphere S ^ n under the influence of a quadratic potential. We will study the case in which this form of degree ?, l + ? has a eigenvalue b_? ... b_l of multiplicities m_? ... m_l. This system is called degenerate if all it's eigenvalues ??are not distinct. The degenerate Neumann system on S ^ n admit a symmetric group. In fact, each group of m_sigma with equal eigenvalues ??gives rise to an O (m_sigma) symmetry in configuration space. The symmetry group G is a direct product of such factors, each action of the factors of this symmetry group has a Ad ^ *-momentum mapping.
