Irreducible tensors in the octahedral spinor group

Abstract

Abstract Irreducible tensorial sets are defined in the octahedral spinor group. These sets have been brought to standard form using Racah's lemma and the operation which effects the transition to contragredience. The importance of using the properties of the invariant triple products to the construction of the highly symmetric 3-Γ symbols in non-simply reducible groups is pointed out and tables of these functions and related invariants are given. A set of formulae, which completes J. S. Griffith's work on the irreducible tensor method for the octahedral group, is derived.