  In this part of our four parts work (e.g see Part I, hep-th/0410242) we use
the theory of polynomial invariants of finite pseudo-reflection groups in order
to reconstruct both the Veneziano and Veneziano-like (tachyon-free) amplitudes
and the generating function reproducing these amplitudes. We demonstrate that
such generating function can be recovered with help of the finite dimensional
exactly solvable N=2 supersymmetric quantum mechanical model known earlier from
works by Witten, Stone and others. Using the Lefschetz isomorphisms theorem we
replace traditional supersymmetric calculations by the group-theoretic thus
solving the Veneziano model exactly using standard methods of representation
theory. Mathematical correctness of our arguments relies on important theorems
by Shepard and Todd, Serre and Solomon proven respectively in early fifties and
sixties and documented in the monograph by Bourbaki. Based on these theorems we
explain why the developed formalism leaves all known results of conformal field
theories unchanged. We also explain why these theorems impose stringent
requirements connecting analytical properties of scattering amplitudes with
symmetries of space-time in which such amplitudes act.
