A Poset Connected to Artin Monoids of Simply Laced Type

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n.Comment: 39 page

Tangle and Brauer Diagram Algebras of Type Dn

A generalization of the Kauffman tangle algebra is given for Coxeter type Dn. The tangles involve a pole or order 2. The algebra is shown to be isomorphic to the Birman-Murakami-Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which in our set-up, occurs when the Coxeter type is of type A with index n-1. The proof involves a diagrammatic version of the Brauer algebra of type Dn in which the Temperley-Lieb algebra of type Dn is a subalgebra.Comment: 33 page

WL | Delft Hydraulics,

Management issues in many sectors of society demand for integrated analysis, which can be supported by integrated modelling. Since the allinclusive modelling software is difficult to achieve, and possibly even undesirable, integrated modelling will require the linkage of individual model or model components that address specific domains. Emerging from the water sector, OpenMI has been developed with the purpose of being the glue which can link legacy and nonlegacy model components from various origins together. OpenMI provides a standardized interface to define, describe and transfer data on a time basis between software components that run simultaneously. This paper presents the technica

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n

A Poset Connected to Artin Monoids of Simply Laced Type

Let W be a Weyl group whose type is a simply laced Dynkin diagram. On several W-orbits of sets of mutually commuting reflections, a poset is described which plays a role in linear representatons of the corresponding Artin group A. The poset generalizes many properties of the usual order on positive roots of W given by height. In this paper, a linear representation of the positive monoid of A is defined by use of the poset

Tangle and Brauer diagram algebras of type D_n

A generalization of the Kauffman tangle algebra is given for Coxeter type D_n. The tangles involve a pole of order 2. The algebra is shown to be isomorphic to the Birman–Murakami–Wenzl algebra of the same type. This result extends the isomorphism between the two algebras in the classical case, which, in our set-up, occurs when the Coxeter type is A_(n - 1). The proof involves a diagrammatic version of the Brauer algebra of type Dn of which the generalized Temperley–Lieb algebra of type D_n is a subalgebra

OpenMI: the essential concepts and their implications for legacy software

International audienceInformation & Communication Technology (ICT) tools such as computational models are very helpful in designing river basin management plans (rbmp-s). However, in the scientific world there is consensus that a single integrated modelling system to support e.g. the implementation of the Water Framework Directive cannot be developed and that integrated systems need to be very much tailored to the local situation. As a consequence there is an urgent need to increase the flexibility of modelling systems, such that dedicated model systems can be developed from available building blocks. The HarmonIT project aims at precisely that. Its objective is to develop and implement a standard interface for modelling components and other relevant tools: The Open Modelling Interface (OpenMI) standard. The OpenMI standard has been completed and documented. It relies entirely on the "pull" principle, where data are pulled by one model from the previous model in the chain. This paper gives an overview of the OpenMI standard, explains the foremost concepts and the rational behind it

A high‐throughput Raman notch filter set

A chevron‐type Raman notch filter (RNF) set is described. lt combines a high signal throughput (up to 90% around 1600 cm−1 and ≳80% between and 700 and 2700 cm−1) with a laser line suppression of 108–109. The filter set can be used to replace the first two dispersion stages in triple‐stage Raman monochromators commonly employed in multichannel detection systems. This yields a gain in intensity of the detected Raman signal of a factor of 4. It is shown that in Raman spectrometers with a backscatter geometry, the filter set can also be used to optically couple the microscope and the spectrometer. This leads to a further increase in signal intensity of a factor of 3–4 as compared to the situation where a beam splitter is used. Additional advantages of the RNF set are the fact that signal throughput is almost polarization independent over a large spectral interval and that it offers the possibility to simultaneously record Stokes and anti‐Stokes spectra