  Generalizing Jones's notion of a planar algebra, we have previously
introduced an A_2-planar algebra capturing the structure contained in the
double complex pertaining to the subfactor for a finite SU(3) ADE graph with a
flat cell system. We now introduce the notion of modules over an A_2-planar
algebra, and describe certain irreducible Hilbert A_2-TL-modules. We construct
an A_2-graph planar algebra associated to each pair (G,W) given by an SU(3) ADE
graph G and a cell system W on G. A partial modular decomposition of these
A_2-graph planar algebras is achieved.
