Characters for from a novel thermodynamic Bethe ansatz

Motivated by the recent development on the exact thermodynamics of one-dimensional quantum systems, we propose quasiparticle-like formulae for characters. The case is re-examined first. The novel formulation yields a direct connection to the fractional statistics in the short-range interacting model, and provides a clear description of the spinon character formula. Generalizing the observation, we find formulae for , which can be proved by the Durfee rectangle formula.