SU( N) lattice integrable models associated with graphs

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...

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Bibliographic Details
Published inNuclear physics. B Vol. 338; no. 3; pp. 602 - 646
Main Authors Di Francesco, P., Zuber, J.-B.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 16.07.1990
Elsevier
Subjects
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
Theory of quantized fields
Eigenvalue
SU(N) group
Field theory
Lie algebra
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Summary: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.
ISSN:0550-3213
1873-1562
DOI:10.1016/0550-3213(90)90645-T