Commuting charges and symmetric spaces

Every classical sigma-model with target space a compact symmetric space $G\mathrm{/}H$ (with $G$ classical) is shown to possess infinitely many local, commuting, conserved charges which can be written in closed form. The spins of these charges run over a characteristic set of values, playing the role of exponents of $G\mathrm{/}H$, and repeating modulo an integer $h$ which plays the role of a Coxeter number.