2,163 research outputs found
Spectral Measures for
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 and its double cover the compact
connected, simply-connected rank two Lie group , including the McKay
graphs for the irreducible representations of and and their
maximal tori, and fusion modules associated to the modular invariants.Comment: 41 pages, 45 figures. Title changed and notation corrected. arXiv
admin note: substantial text overlap with arXiv:1404.186
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
Spectral Measures for II: finite subgroups
Joint spectral measures associated to the rank two Lie group , including
the representation graphs for the irreducible representations of and its
maximal torus, nimrep graphs associated to the 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 . Using character
theoretic methods we classify all non-conjugate embeddings of each subgroup
into the fundamental representation of 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
Spectral Measures for
Spectral measures provide invariants for braided subfactors via fusion
modules. In this paper we study joint spectral measures associated to the rank
two Lie group , including the McKay graphs for the irreducible
representations of and its maximal torus, and fusion modules associated
to all known modular invariants.Comment: 36 pages, 40 figures; correction to Sections 5.4 and 5.5, minor
improvements to expositio
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Exploring teaching Shakespeare with fan fiction
Although students are exposed to the works of Shakespeare extensively from 9th -12th grade and sometimes at the postsecondary level, teachers are pressed to make the literature relevant and interesting for their classes. Fan fiction, which are stories written by amateurs out of a strong feeling of admiration and appreciation for an existing work, present numerous avenues to engage students with classic literature. I developed a fan fiction website called the Stratford Tattler which reimagines Shakespeare’s characters and world as if they were modern day celebrities which the website covers like an online tabloid. While I wrote fan fiction articles and developed the website, I received feedback, which in turn formed an iterative design. Three university Shakespeare scholars, two high school English teachers, and one legal expert on copyright provided the bulk of the feedback and advice. Over six months, I incorporated their suggestions as the project evolved from trying to build a participatory community to developing a stand-alone learning environment which teachers could readily incorporate in their classroom. The final result includes a website with teacher resources, namely a teacher’s guide with recommendations and lesson plans directed at high school English teachers, along with a model article of fan fiction that stays true to Shakespeare’s original text, a quality that most of the aforementioned experts who participated in the project found necessary for fan fiction to be educational. The teacher’s guide also includes guidelines for avoiding copyright infringement when repurposing existing digital images. Along with these teacher resources, the insights of my participants and my experience writing fan fiction as related in this report hopefully provide a first step toward high school English teachers being create their own fan fiction website and engage students with classic literature.Curriculum and Instructio
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
Classification of Module Categories for
The main goal of this paper is to classify -module categories for the
modular tensor category. This is done by classifying
nimrep graphs and cell systems, and in the process we also classify the
modular invariants. There are module categories of type ,
and their conjugates, but there are no orbifold (or type
) module categories. We present a construction of a subfactor with
principal graph given by the fusion rules of the fundamental generator of the
modular category. We also introduce a Frobenius algebra which
is an generalisation of (higher) preprojective algebras, and derive a
finite resolution of as a left -module along with its Hilbert series.Comment: 56 pages, many figures; corrected error at the end of Section 4 about
nimrep, and corrected computational error in Theorem 5.10
about . The main theorem, Theorem 5.12, has been modified to
reflect these correction
A characterization of visual feature recognition
technical reportNatural human interfaces are a key to realizing the dream of ubiquitous computing. This implies that embedded systems must be capable of sophisticated perception tasks. This paper analyzes the nature of a visual feature recognition workload. Visual feature recognition is a key component of a number of important applications, e.g. gesture based interfaces, lip tracking to augment speech recognition, smart cameras, automated surveillance systems, robotic vision, etc. Given the power sensitive nature of the embedded space and the natural conflict between low-power and high-performance implementations, a precise understanding of these algorithms is an important step developing efficient visual feature recognition applications for the embedded space. In particular, this work analyzes the performance characteristics of flesh toning, face detection and face recognition codes based on well known algorithms. We also show how the problem can be decomposed into a pipeline of filters that have efficient implementations as stream processors
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