  Two-dimensional conformal field theories with just Virasoro symmetry are
endowed with integrable structure. We review how to construct the integrable
charges in a two-dimensional conformal field theory and how to relate them to
the charges of quantum Sinh-Gordon theory when c>25. We then explicitly
calculate the single charge characters in the large c limit for all charges and
thereby reveal how their degeneracies grow within one module. This, in
particular, allows us to approximate the characters in the limit of small
chemical potential, which source the respective charges. The latter give us
insights into possible transformation properties of the characters. We also
comment on the full generalized Gibbs ensemble and approximations to pure
states.

High Energy Physics - Theory;Statistical Mechanics