Representation-theoretic derivation of the Temperley-Lieb-Martin algebras

Explicit expressions for the Temperley-Lieb-Martin algebras, i.e., the quotients of the Hecke algebra that admit only representations corresponding to Young diagrams with a given maximum number of columns (or rows), are obtained, making explicit use of the Hecke algebra representation theory. Similar techniques are used to construct the algebras whose representations do not contain rectangular subdiagrams of a given size.Comment: 12 pages, LaTeX, to appear in J. Phys.

Topological Quantum Field Theories and Operator Algebras

We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.Comment: For proceedings of "International Workshop on Quantum Field Theory and Noncommutative Geometry", Sendai, November 200

Quantum Gravity and the Algebra of Tangles

In Rovelli and Smolin's loop representation of nonperturbative quantum gravity in 4 dimensions, there is a space of solutions to the Hamiltonian constraint having as a basis isotopy classes of links in R^3. The physically correct inner product on this space of states is not yet known, or in other words, the *-algebra structure of the algebra of observables has not been determined. In order to approach this problem, we consider a larger space H of solutions of the Hamiltonian constraint, which has as a basis isotopy classes of tangles. A certain algebra T, the ``tangle algebra,'' acts as operators on H. The ``empty state'', corresponding to the class of the empty tangle, is conjectured to be a cyclic vector for T. We construct simpler representations of T as quotients of H by the skein relations for the HOMFLY polynomial, and calculate a *-algebra structure for T using these representations. We use this to determine the inner product of certain states of quantum gravity associated to the Jones polynomial (or more precisely, Kauffman bracket).Comment: 16 pages (with major corrections

The Nakayama automorphism of the almost Calabi-Yau algebras associated to SU(3) modular invariants

We determine the Nakayama automorphism of the almost Calabi-Yau algebra A associated to the braided subfactors or nimrep graphs associated to each SU(3) modular invariant. We use this to determine a resolution of A as an A-A bimodule, which will yield a projective resolution of A.Comment: 46 pages which constitutes the published version, plus an Appendix detailing some long calculations. arXiv admin note: text overlap with arXiv:1110.454

A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)

A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.Comment: Latex, 11 pages, no figure

Anomalous Scale Dimensions from Timelike Braiding

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields of anomalous scaling dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions. Starting from the old observations on conformal superselection sectors related to the anomalous dimensions via the phases which appear in the spectral decomposition of the center of the conformal covering group $Z(\widetilde{SO(d,2)}),$ we explore the possibility of a timelike braiding structure consistent with the timelike ordering which refines and explains the central decomposition. We regard this as a preparatory step in a new construction attempt of interacting conformal quantum field theories in D=4 spacetime dimensions. Other ideas of constructions based on the $AdS_{5}$-$CQFT_{4}$ or the perturbative SYM approach in their relation to the present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages tcilatex, 3 latexcad figure

Association mapping of spot blotch resistance in wild barley

Spot blotch, caused by Cochliobolus sativus, is an important foliar disease of barley. The disease has been controlled for over 40 years through the deployment of cultivars with durable resistance derived from the line NDB112. Pathotypes of C. sativus with virulence for the NDB112 resistance have been detected in Canada; thus, many commercial cultivars are vulnerable to spot blotch epidemics. To increase the diversity of spot blotch resistance in cultivated barley, we evaluated 318 diverse wild barley accessions comprising the Wild Barley Diversity Collection (WBDC) for reaction to C. sativus at the seedling stage and utilized an association mapping (AM) approach to identify and map resistance loci. A high frequency of resistance was found in the WBDC as 95% (302/318) of the accessions exhibited low infection responses. The WBDC was genotyped with 558 Diversity Array Technology (DArT®) and 2,878 single nucleotide polymorphism (SNP) markers and subjected to structure analysis before running the AM procedure. Thirteen QTL for spot blotch resistance were identified with DArT and SNP markers. These QTL were found on chromosomes 1H, 2H, 3H, 5H, and 7H and explained from 2.3 to 3.9% of the phenotypic variance. Nearly half of the identified QTL mapped to chromosome bins where spot blotch resistance loci were previously reported, offering some validation for the AM approach. The other QTL mapped to unique genomic regions and may represent new spot blotch resistance loci. This study demonstrates that AM is an effective technique for identifying and mapping QTL for disease resistance in a wild crop progenitor

Ambient fabrication of flexible and large-area organic light-emitting devices using slot-die coating

The grand vision of manufacturing large-area emissive devices with low-cost roll-to-roll coating methods, akin to how newspapers are produced, appeared with the emergence of the organic light-emitting diode about 20 years ago. Today, small organic light-emitting diode displays are commercially available in smartphones, but the promise of a continuous ambient fabrication has unfortunately not materialized yet, as organic light-emitting diodes invariably depend on the use of one or more time- and energy-consuming process steps under vacuum. Here we report an all-solution-based fabrication of an alternative emissive device, a light-emitting electrochemical cell, using a slot-die roll-coating apparatus. The fabricated flexible sheets exhibit bidirectional and uniform light emission, and feature a fault-tolerant >1-μm-thick active material that is doped in situ during operation. It is notable that the initial preparation of inks, the subsequent coating of the constituent layers and the final device operation all could be executed under ambient air