Spectral Measures of Small Index Principal Graphs
نویسندگان
چکیده
Abstract. The principal graph X of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If ∆ is the adjacency matrix of X we consider the equation ∆ = U + U. When X has square norm ≤ 4 the spectral measure of U can be averaged by using the map u → u, and we get a probability measure ε on the unit circle which does not depend on U . We find explicit formulae for this measure ε for the principal graphs of subfactors with index ≤ 4, the (extended) Coxeter-Dynkin graphs of type A, D and E. The moment generating function of ε is closely related to Jones’ Θ-series.
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تاریخ انتشار 2006