ON INDUCED SCALAR PRODUCTS AND UNITARIZATION

Infinitesimal unitarity of representations of the simple real Lie algebras su (2), su (1,1), and so(4) is discussed with respect to scalar products induced by sesquilinear forms on their universal enveloping algebras. Sesquilinear forms are explicitly calculated. The Verma modules, their irreducible quotients, their irreducible submodules, and their infinitesimal unitarizability are discussed. © 1990 American Institute of Physics.