Spectral Measures of Small Index Principal Graphs |
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| Authors: | Teodor Banica Dietmar Bisch |
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| Institution: | (1) Department of Mathematics, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France;(2) Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37240, USA |
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| Abstract: | The principal graph X of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If Δ is the adjacency matrix of X we consider the equation Δ = U + U
−1. When X has square norm ≤ 4 the spectral measure of U can be averaged by using the map u→ u
−1, and we get a probability measure
 on the unit circle which does not depend on U. We find explicit formulae for this measure
 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
 is closely related to Jones’ Θ-series.D.B. was supported by NSF under Grant No. DMS-0301173. |
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