Tableaux and insertion schemes for spinor representations of the orthogonal Lie algebra so(2 r + 1, ℂ)

A new set of tableaux is presented to index the weights of the irreducible spinor representations of the orthogonal Lie algebra so(2 r + 1, ℂ). These tableaux are used to develop insertion schemes which combinatorially describe the decomposition of the tensor product of the spin representation with an irreducible representation of so(2 r + 1, ℂ).