On State Counting and Characters

We outline the relationship between the thermodynamic densities and quasi-particle descriptions of spectra of RSOS models with an underlying Bethe equation. We use this to prove completeness of states in some cases and then give an algorithm for the construction of branching functions of their emergent conformal field theories. Starting from the Bethe equations of $D_n$ type, we discuss some aspects of the $Z_n$ lattice models.

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