We explore the construction of RSOS critical integrable models attached to a graph, trying to extend Pasquier's construction from SU(2) to SU(N), with main emphasis on the case of SU(3): the heights are the nodes of a graph, which encodes the allowed configurations. A class of graphs that are natural candidates for this construction is defined. In the case N = 3, they all seem to be related to finite subgroups of SU(3). For any N, they are associated with arbitrary representations of the SU(N) fusion algebra over matrices of non-negative integers. It is argued that these graphs should support a representation of the Hecke algebra.
ASJC Scopus subject areas
- Nuclear and High Energy Physics