It is shown that the Berry phase/matrix for Hamiltonians parametrized
by the points of M=SU(n)/S(U(1)XU(n - 1)) and having no accidental deg
eneracy is expressible in terms of Riemannian connection on M and repr
esentations of S(U(1) xU(n - 1)). (C) 1996 American Institute of Physi
cs.