Weyl group and tensor operators for hadron-type SU(n) representations

Abstract

Let a particle symmetry be described by a simple Lie algrebra 𝔤 of the type An−1, i.e., 𝔤=sl(n,C) or 𝔤 is a real form of sl(n,C). For 𝔤 representations describing three-particle or particle–antiparticle states, relationships between two actions, the action of 𝔤 and the action of the corresponding Weyl group Sn, on observables are analyzed. It is shown, in particular, how impossible physical relations depend on these two actions. The results enable one to verify quickly if given experimental data can be fitted by means of a 𝔤-symmetry theory.