Primitive representations of the SL(3,R) algebra

Unitary irreducible representations of the SL(3,R) algebra each containing not more than once an irreducible representation of the SO(3) algebra are investigated. The possibility of using the primitive representations ASL(3,R) to reproduce the Regge classification is explored. All the representations obtained and all the irreducible unitary representations of the Lorentz group algebra are realized. This realization is based on the formalism of creaction and annihilation operators. It is very compact and obvious method