Abstract

Generalizing Jonesʼs 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.

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