  The endoscopic classification via the stable trace formula comparison
provides certain character relations between irreducible cuspidal automorphic
representations of classical groups and their global Arthur parameters, which
are certain automorphic representations of general linear groups. It is a
question of J. Arthur and W. Schmid that asks: How to construct concrete
modules for irreducible cuspidal automorphic representations of classical
groups in term of their global Arthur parameters? In this paper, we formulate a
general construction of concrete modules, using Bessel periods, for cuspidal
automorphic representations of classical groups with generic global Arthur
parameters. Then we establish the theory for orthogonal and unitary groups,
based on certain well-expected conjectures. Among the consequences of the
theory in this paper is that the global Gan-Gross-Prasad conjecture for those
classical groups is proved in full generality in one direction and with a
global assumption in the other direction.
