  We obtain inductive and enumerative formulas for the multiplicities of the
weights of the spin module for the Clifford algebra of a Levi subalgebra in a
complex semisimple Lie algebra. Our formulas involve only matrices and
tableaux, and our techniques combine linear algebra, Lie theory, and
combinatorics. Moreover, this suggests a relationship with complex nilpotent
orbits. The case of the special linear Lie algebra $\mathfrak{sl}(n,{\mathbb
C})$ is emphasized.
