A semigroup contained in SL$_{2R}$ complex angular momentum

The authors study the relevant geometrical properties and a class of linear representations of a semigroup S contained in SL/sub 2R/. These representations can be used in order to partially diagonalize the multiperipheral integral equation for spacelike four-momentum transfer. Moreover, they can be used for the harmonic analysis of some absorptive multiparticle amplitudes, which can be considered as functions on S. They get in this way a new approach to complex angular momentum, which has many advantages and in particular permits them to interpret some peculiar phenomena as the Gell-Mann compensating mechanism and the Mandelstam twin symmetry. (27 refs).