Irreducible decompositions of physical tensors of high orders

In this paper we use the term 'physical tensor' to stand for a tensor that belongs to a tensor subspace. Based on the relationship among the character s of rotation representation, some techniques are developed in order to giv e the numbers of independent deviatoric tensors contained in the irreducibl e decompositions of physical tensors, even prior to the constructions of th e irreducible decompositions. A number of examples are shown and many of th em are new results.