Kronecker Products Which Decompose into Two Irreducible Representations

摘要

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 ((m lambda /sub 1/), ( lambda sub(n)) for algebras of type Bsub(n), (( lambda /sub 1/), (m lambda sub(n)) for algebras of type Csub(n), and ((m lambda /sub 1/), ( lambda sub(n-1)), ((m lambda /sub 1/), ( lambda sub(n)), (( lambda /sub 1/), (m lambda sub(n-1)), (( lambda /sub 1/), (m lambda sub(n)) for algebras of type Dsub(n)3/where lambda sub(i) denotes the highest weight of the fundamental representation ( lambda sub(i)) and m is an arbitrary positive integer. 9 refs. (Atomindex citation 18:003097)