  In 1997 Bousquet-M\'elou and Eriksson introduced lecture hall partitions as
the inversion vectors of elements of the parabolic quotient $\widetilde{C}/C$.
We provide a new view of their correspondence that allows results in one domain
to be translated into the other. We determine the equivalence between
combinatorial statistics in each domain and use this correspondence to
translate certain generating function formulas on lecture hall partitions to
new observations about $\widetilde{C}/C$.
