The direct sum decomposition of tensor products for has many applications in physics, and the problem has been studied extensively. This has resulted in many decomposition methods, each with its advantages and disadvantages. The description given here is geometric in nature and it describes both the constituents of the direct sum and their multiplicities. In addition to providing decompositions of specific tensor products, this approach is very well suited to studying tensor products as the parameters vary and helping draw general conclusions. After a description and proof of the method, several consequences are discussed and proved. In particular, questions regarding multiplicities are considered.
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