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

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.Comment: 47 pages, minor changes, to appear in Reviews in Mathematical Physic

In-flight friction and wear mechanism

A unique mechanism developed for conducting friction and wear experiments in orbit is described. The device is capable of testing twelve material samples simultaneously. Parameters considered critical include: power, weight, volume, mounting, cleanliness, and thermal designs. The device performed flawlessly in orbit over an eighteen month period and demonstrated the usefulness of this design for future unmanned spacecraft or shuttle applications

Integrable Lattice Models for Conjugate An(1)A^{(1)}_n

A new class of $A^{(1)}_n$ integrable lattice models is presented. These are interaction-round-a-face models based on fundamental nimrep graphs associated with the $A^{(1)}_n$ conjugate modular invariants, there being a model for each value of the rank and level. The Boltzmann weights are parameterized by elliptic theta functions and satisfy the Yang-Baxter equation for any fixed value of the elliptic nome q. At q=0, the models provide representations of the Hecke algebra and are expected to lead in the continuum limit to coset conformal field theories related to the $A^{(1)}_n$ conjugate modular invariants.Comment: 18 pages. v2: minor changes, such as page 11 footnot

The Federal Aviation Administration/Massachusetts Institute of Technology (FAA/MIT) Lincoln Laboratory Doppler weather radar program

The program focuses on providing real-time information on hazardous aviation weather to end users such as air traffic control and pilots. Existing systems will soon be replaced by a Next Generation Weather Radar (NEXRAD), which will be concerned with detecting such hazards as heavy rain and hail, turbulence, low-altitude wind shear, and mesocyclones and tornadoes. Other systems in process are the Central Weather Processor (CWP), and the terminal Doppler weather radar (TDWR). Weather measurements near Memphis are central to ongoing work, especially in the area of microbursts and wind shear

Trace-scaling automorphisms of certain stable AF algebras

Trace scaling automorphisms of stable AF algebras with dimension group totally ordered are outer conjugate if the scaling factors are the same (not equal to one). This is an adaptation of a similar result for the AFD type II_infty factor by Connes and extends the previous result for stable UHF algebras.Comment: 12 pages, late

Spectral Measures for Sp(2)Sp(2)

Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the compact connected rank two Lie group $SO(5)$ and its double cover the compact connected, simply-connected rank two Lie group $Sp(2)$, including the McKay graphs for the irreducible representations of $Sp(2)$ and $SO(5)$ and their maximal tori, and fusion modules associated to the $Sp(2)$ modular invariants.Comment: 41 pages, 45 figures. Title changed and notation corrected. arXiv admin note: substantial text overlap with arXiv:1404.186

Modular Invariants from Subfactors: Type I Coupling Matrices and Intermediate Subfactors

A braided subfactor determines a coupling matrix Z which commutes with the S- and T-matrices arising from the braiding. Such a coupling matrix is not necessarily of "type I", i.e. in general it does not have a block-diagonal structure which can be reinterpreted as the diagonal coupling matrix with respect to a suitable extension. We show that there are always two intermediate subfactors which correspond to left and right maximal extensions and which determine "parent" coupling matrices Z^\pm of type I. Moreover it is shown that if the intermediate subfactors coincide, so that Z^+=Z^-, then Z is related to Z^+ by an automorphism of the extended fusion rules. The intertwining relations of chiral branching coefficients between original and extended S- and T-matrices are also clarified. None of our results depends on non-degeneracy of the braiding, i.e. the S- and T-matrices need not be modular. Examples from SO(n) current algebra models illustrate that the parents can be different, Z^+\neq Z^-, and that Z need not be related to a type I invariant by such an automorphism.Comment: 25 pages, latex, a new Lemma 6.2 added to complete an argument in the proof of the following lemma, minor changes otherwis

Spectral Measures for G2G_2 II: finite subgroups

Joint spectral measures associated to the rank two Lie group $G_2$, including the representation graphs for the irreducible representations of $G_2$ and its maximal torus, nimrep graphs associated to the $G_2$ modular invariants have been studied. In this paper we study the joint spectral measures for the McKay graphs (or representation graphs) of finite subgroups of $G_2$. Using character theoretic methods we classify all non-conjugate embeddings of each subgroup into the fundamental representation of $G_2$ and present their McKay graphs, some of which are new.Comment: 33 pages, 20 figures; minor improvements to exposition. Accepted for publication in Reviews in Mathematical Physic

Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants

Braided subfactors of von Neumann algebras provide a framework for studying two dimensional conformal field theories and their modular invariants. We review this in the context of SU(3) conformal field theories through corresponding SU(3) braided subfactors and various subfactor invariants including spectral measures for the nimrep graphs, A_2-planar algebras and almost Calabi-Yau algebras.Comment: 45 pages, 25 figures. v3: minor correction to Figure 14; v2: figures of 0-1 parts of graphs included, some minor correction