Orthogonal irreducible decompositions of tensors of high orders

It is known from the theory of group representations that, in principle, a tenser of any finite order can be decomposed into a sum of irreducible tens ors. This paper develops a simple and effective recursive method to realize such decompositions in both two- and three-dimensional spaces. Particularl y, such derived decompositions have mutually orthogonal base elements. Quit e a few application examples are given for generic and various physical ten sors of orders up to six.