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Mathew Pugh

  1. Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3).

    Fri, 02/12/2010 - 16:01 — SomNambul
    Authors: David E. Evans, Mathew Pugh
    Subjects: Operator Algebras
    Abstract

    We complete the computation of spectral measures for SU(3) nimrep graphs
    arising in subfactor theory, namely the SU(3) ADE graphs associated with SU(3)
    modular invariants and the McKay graphs of finite subgroups of SU(3). For the
    SU(2) graphs the spectral measures distill onto very special subsets of the
    semicircle/circle, whilst for the SU(3) graphs the spectral measures distill
    onto very special subsets of the discoid/torus. The theory of nimreps allows us
    to compute these measures precisely.

  2. Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: David E. Evans, Mathew Pugh
    Subjects: Operator Algebras
    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.

  3. SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: David E. Evans, Mathew Pugh
    Subjects: Operator Algebras
    Abstract

    We complete the realisation by braided subfactors, announced by Ocneanu, of
    all SU(3)-modular invariant partition functions previously classified by
    Gannon.

  4. Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: David E. Evans, Mathew Pugh
    Subjects: Operator Algebras
    Abstract

    We determine the cells, whose existence has been announced by Ocneanu, on all
    the candidate nimrep graphs except $\mathcal{E}_4^{(12)}$ proposed by di
    Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This
    enables the Boltzmann weights to be computed for the corresponding integrable
    statistical mechanical models and provide the framework for studying
    corresponding braided subfactors to realise all the SU(3) modular invariants as
    well as a framework for a new SU(3) planar algebra theory.

  5. Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs.

    Thu, 09/03/2009 - 17:38 — SomNambul
    Authors: David E. Evans, Mathew Pugh
    Subjects: Operator Algebras
    Abstract

    We determine the cells, whose existence has been announced by Ocneanu, on all
    the candidate nimrep graphs except $\mathcal{E}_4^{(12)}$ proposed by di
    Francesco and Zuber for the SU(3) modular invariants classified by Gannon. This
    enables the Boltzmann weights to be computed for the corresponding integrable
    statistical mechanical models and provide the framework for studying
    corresponding braided subfactors to realise all the SU(3) modular invariants as
    well as a framework for a new SU(3) planar algebra theory.

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