$SL(2,R)$ symmetry of dual two-particle amplitude

Dispersion relations are used to represent the crossing-symmetric scattering amplitude of two scalar particles as a Mellin integral. The amplitude's duality derives from its being symmetric under irreducible unitary representations of $SL(2,R)$. The symmetry makes it possible to find an integral representation for the dual amplitude, this serving to combine the properties of duality and unitarity.