Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory

Abstract

We determine spectral measures for some nimrep graphs arising in subfactor theory, particularly those associated with SU(3) modular invariants and subgroups of SU(3). Our methods also give an alternative approach to deriving the results of Banica and Bisch for ADE graphs and subgroups of SU(2) and explain the connection between their results for affine ADE graphs and the Kostant polynomials. We also look at the Hilbert generating series of associated pre-projective algebras.

54 pages, 15 figures, result on page 50 corrected, to appear in Communications in Mathematical Physics

References in corpus (3)

• Spectral measures of small index principal graphs
• SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants
• Cyclotomic expansion of exceptional spectral measures

Cited by in corpus (6)

• The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants
• Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3)
• Spectral Measures for $G_2$
• $K$-theory of AF-algebras from braided C*-tensor categories
• Spectral measures associated to rank two Lie groups and finite subgroups of $GL(2,\mathbb{Z})$
• Principles of operator algebras