David E. Evans
Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries.
Thu, 12/09/2010 - 16:01 — SomNambulAuthors: David E. Evans, Terry Gannon
Subjects: K-Theory and Homology
AbstractThe modular invariant partition functions of conformal field theory (CFT)
have a rich interpretation within von Neumann algebras (subfactors), which has
led to the development of structures such as the full system (fusion ring of
defect lines), nimrep (cylindrical partition function), alpha-induction, etc.
Modular categorical interpretations for these have followed. More recently,
Freed-Hopkins-Teleman have expressed the Verlinde ring of conformal field
theories associated to loop groups as twisted equivariant K-theory. For the
generic families of modular invariants (i.e.Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory II: SU(3).
Fri, 02/12/2010 - 16:01 — SomNambulAuthors: David E. Evans, Mathew Pugh
Subjects: Operator Algebras
AbstractWe 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.Spectral Measures and Generating Series for Nimrep Graphs in Subfactor Theory.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: David E. Evans, Mathew Pugh
Subjects: Operator Algebras
AbstractWe 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.SU(3)-Goodman-de la Harpe-Jones subfactors and the realisation of SU(3) modular invariants.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: David E. Evans, Mathew Pugh
Subjects: Operator Algebras
AbstractWe complete the realisation by braided subfactors, announced by Ocneanu, of
all SU(3)-modular invariant partition functions previously classified by
Gannon.Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: David E. Evans, Mathew Pugh
Subjects: Operator Algebras
AbstractWe 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.Ocneanu Cells and Boltzmann Weights for the SU(3) ADE Graphs.
Thu, 09/03/2009 - 17:38 — SomNambulAuthors: David E. Evans, Mathew Pugh
Subjects: Operator Algebras
AbstractWe 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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