  Global dimensions for fusion categories defined by a pair (G,k), where G is a
Lie group and k a positive integer, are expressed in terms of Lie quantum
superfactorial functions. The global dimension is defined as the square sum of
quantum dimensions of simple objects, for the category of integrable modules
over an affine Lie algebra at some level. The same quantities can also be
defined from the theory of quantum groups at roots of unity or from conformal
field theory WZW models. Similar results are also presented for those
associated module-categories that can be obtained via conformal embeddings
(they are "quantum subgroups" of a particular kind). As a side result, we
express the classical (or quantum) Weyl denominator of simple Lie groups in
terms of products of classical (or quantum) factorials calculated for the
exponents of the group. Some calculations use the correspondence existing
between periodic quivers for simply-laced Lie groups and fusion rules for
module-categories (alias nimreps) of type SU(2).
