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To every simple Lie group G one can associate both a quantum and a classical superfactorial of type G.
The classical Lie superfactorial of type G, denoted sf_G, is defined as the classical limit (q-->1) of the quantum Weyl denominator of G.
If G is simply laced (ADE Dynkin diagrams) ie Ar,Dr,E6,E7,E8 cases, the integer sf_G is the product of s!, where s runs over the multiset of exponents of G.
The usual superfactorial r --> sf[r] is recovered as the Lie superfactorial r --> sf_{Ar} of type Ar [nonascii characters here] SU(r+1), sequence A000178.
The given sequence is the Lie superfactorial of type Dr: r --> sf_{Dr} = (g/2)! Product_{s in 1,3,5,... g-1} s! , with g = 2r-2.
If G is exceptional of type E, the Lie superfactorial does not define an infinite sequence (see A169667).
If G is not simply laced, ie (Br, Cr, G2, F4) cases, the Lie superfactorial is also simply related to the product of factorials s! where s belongs to the multiset E of exponents of G. See sequences A169668.
The classical Lie superfactorial of type G enters the asymptotic expression giving the global dimension of a monoidal category of type G at level k, when k is large.
Call r the rank of G, gamma its Coxeter number, Delta the determinant of the fundamental quadratic form, and dim(G) its dimension, the asymptotic expression reads : k^dim(G) / ((2 pi)^(r gamma) Delta (sf_G)^2 ).
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