Essential paths space on ADE SU(3) graphs: A geometric approach
  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. 
Jesus A. Pineda, E. Isasi and M. I. Caicedo
math-ph math.MP