STATISTICAL-MECHANICAL INTERPRETATION OF THE INVERSE SCATTERING METHOD - LEVEL DYNAMICS FOR EXCLUSION STATISTICS

Considered is the relationship between the level dynamics and the inte grable differential-difference equation. By applying the inverse scatt ering method to the Bogoyavlensky lattice, which is an extension of th e Volterra model, the role of the exclusion statistics is clarified. E ach dynamical variable is identified with an energy level. Briefly dis cussed is a generalization of the Yangian symmetric system, and the '' Gentile'' statistics is revealed.