Kronecker products which decompose into two irreducible representations

The aim of the work is to determine, for the semisimple Lie algebra of types Bsub(n), Csub(n) and Dsub(n) sets of pairs of irreducible representations having the property that the Kronecker product of the representations of each pair decomposes into a direct sum of two irreducible representations. The proof uses Dynkin theorem and a calculation of dimensionalities. The pairs of representations obtained in this way are ((mΛ1), (Λsub(n)) for algebras of type Bsub(n), ((Λ1), (mΛsub(n)) for algebras of type Csub(n), and ((mΛ1), (Λsub(n-1)), ((mΛ1), (Λsub(n)), ((Λ1), (mΛsub(n-1)), ((Λ1), (mΛsub(n)) for algebras of type Dsub(n)3/where Λ sub(i) denotes the highest weig.ht of the fundamental representation (Λsub(i)) and m is an arbitrary positive integer