Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory

TL;DR

This paper analyzes spectral measures and generating series for nimrep graphs in subfactor theory, connecting them with SU(3) invariants, ADE graphs, and Kostant polynomials, offering new insights and methods.

Contribution

It introduces an alternative approach to spectral measures for nimrep graphs and links various algebraic structures in subfactor theory.

Findings

Spectral measures for SU(3) related nimrep graphs are explicitly determined.

Provides an alternative derivation for ADE graph spectral results.

Explores connections between Hilbert series, Kostant polynomials, and subfactor invariants.

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.