Essential paths space on ADE SU(3) graphs: A geometric approach

Abstract

For simply laced SU (3) graphs we offer a geometric understanding of the path creation and annihilation operators for SU (3) in terms of creation and annihilation of sequences of three vertices forming triangular cells or collapsed triangular cells. We prove that the space of paths of a given length can be decomposed as a direct sum of orthogonal sub-spaces constructed by recurrent applications of the path creation operator on subspaces of essential paths of shorter length.