Multiplet classification of the reducible elementary representations of real semisimple Lie groups: The \(SO_ e(p,q)\) example (Q1061251)

A multiplet classification of the reducible elementary representations \((=generalized\) principal series representations) is proposed as a useful intermediate step in the important problem of determining the irreducible composition factors of the elementary representations and their multiplicities and, thus, of the distribution characters of all irreducible representations of real semisimple Lie groups. As an example, the results for the elementary representations of SO\({}_ e(p,q)\) induced from its minimal parabolic subgroup are given. Further research is also indicated.