Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory

The SU(n) quantum chains with inverse-square exchange exhibit a novel form of Yangian symmetry compatible with periodic boundary conditions, allowing states to be countable. We characterize the "supermultiplets" of the spectrum in terms of generalized "occupation numbers." We embed the model in the k=1 SU(n) Kac-Moody algebra and obtain a new classification of the states of conformal field theory, adapted to particlelike elementary excitations obeying fractional statistics.