Branching rules for classical Lie groups using tensor and spinor methods

Tensor and spinor methods are used to derive branching rule formulae for the embedding of one classical Lie group in another. These formulae involve operations on S-functions. By the judicious use of identities satisfied by certain infinite series of S-functions, they are reduced to forms which may be used very efficiently. Eleven sets of the branching rule formulae derived are as simple as possible, in that they involve only a sum of positive terms, whilst four other sets involve some negative terms which ultimately cancel. The advantage of using a composite notation, both for mixed tensor and for spinor representations, is made apparent. A comparison is made with methods used to derive branching rules based on mapping from one weight space to another.