Hierarchies of invariant spin models Original Research Article

In this paper we present classes of state sum models based on the recoupling theory of angular momenta of SU(2) (and of its q-counterpart Uq(sl(2)), q a root of unity). Such classes are arranged in hierarchies depending on the dimension d, and include all known closed models, i.e., the Ponzano–Regge state sum and the Turaev–Viro invariant in dimension d=3, the Crane–Yetter invariant in d=4. In general, the recoupling coefficient associated with a d-simplex turns out to be a {3(d−2)(d+1)/2}j symbol, or its q-analog.