Generating functions for polynomial irreducible tensors

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Abstract
A general method for constructing a generating function for all irreducible polynomial tensors, with respect to a given compact semisimple group, out of a given set of tensors is derived. The method is applied to the construction of polynomial bases for the IR’s of a group reduced according to a subgroup and to the finding of subgroup scalars in the enveloping algebra of a group. A number of examples are worked out.