A Calabi-Yau algebra with E6E_6 symmetry and the Clebsch-Gordan series of sl(3)sl(3)

Building on classical invariant theory, it is observed that the polarised traces generate the centraliser $Z_L(sl(N))$ of the diagonal embedding of $U(sl(N))$ in $U(sl(N))^{\otimes L}$. The paper then focuses on $sl(3)$ and the case $L=2$. A Calabi--Yau algebra $\mathcal{A}$ with three generators is introduced and explicitly shown to possess a PBW basis and a certain central element. It is seen that $Z_2(sl(3))$ is isomorphic to a quotient of the algebra $\mathcal{A}$ by a single explicit relation fixing the value of the central element. Upon concentrating on three highest weight representations occurring in the Clebsch--Gordan series of $U(sl(3))$, a specialisation of $\mathcal{A}$ arises, involving the pairs of numbers characterising the three highest weights. In this realisation in $U(sl(3))\otimes U(sl(3))$, the coefficients in the defining relations and the value of the central element have degrees that correspond to the fundamental degrees of the Weyl group of type $E_6$. With the correct association between the six parameters of the representations and some roots of $E_6$, the symmetry under the full Weyl group of type $E_6$ is made manifest. The coefficients of the relations and the value of the central element in the realisation in $U(sl(3))\otimes U(sl(3))$ are expressed in terms of the fundamental invariant polynomials associated to $E_6$. It is also shown that the relations of the algebra $\mathcal{A}$ can be realised with Heun type operators in the Racah or Hahn algebra.Comment: 24 page

The missing label of su3\mathfrak{su}_3 and its symmetry

We present explicit formulas for the operators providing missing labels for the tensor product of two irreducible representations of $\mathfrak{su}_3$. The result is seen as a particular representation of the diagonal centraliser of $\mathfrak{su}_3$ through a pair of tridiagonal matrices. Using these explicit formulas, we investigate the symmetry of this missing label problem and we find a symmetry group of order 144 larger than what can be expected from the natural symmetries. Several realisations of this symmetry group are given, including an interpretation as a subgroup of the Weyl group of type $E_6$, which appeared in an earlier work as the symmetry group of the diagonal centraliser. Using the combinatorics of the root system of type $E_6$, we provide a family of representations of the diagonal centraliser by infinite tridiagonal matrices, from which all the finite-dimensional representations affording the missing label can be extracted. Besides, some connections with the Hahn algebra, Heun--Hahn operators and Bethe ansatz are discussed along with some similarities with the well-known symmetries of the Clebsch--Gordan coefficients

The Stellar Population Histories of Early-Type Galaxies. II. Controlling Parameters of the Stellar Populations

We analyze single-stellar-population (SSP) equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. These galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], log t, log $\sigma$, and [E/Fe]. SSP age and velocity dispersion can be taken as the two independent parameters that specify a galaxy's location in this ``hyperplane.'' The hyperplane can be decomposed into two sub-relations: (1) a ``Z-plane,'' in which [Z/H] is a linear function of log $\sigma$ and log t; and (2) a relation between [E/Fe] and $\sigma$ in which [E/Fe] is larger in high-$\sigma$ galaxies. Cluster and field ellipticals follow the same hyperplane, but their ($\sigma$,t) distributions within it differ. Nearly all cluster galaxies are old; the field ellipticals span a large range in SSP age. The tight Mg--$\sigma$ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on; the tightness of these relations does not necessarily imply a narrow range of ages at fixed $\sigma$. The relation between [E/Fe] and $\sigma$ is consistent with a higher effective yield of Type II SNe elements at higher $\sigma$. The Z-plane is harder to explain and may be a powerful clue to star formation in elliptical galaxies if it proves to be general. Present data favor a ``frosting'' model in which low apparent SSP ages are produced by adding a small frosting of younger stars to an older base population. If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant $\sigma$ in the Z-plane, as required. This favors star formation from well-mixed pre-enriched gas rather than unmixed low-metallicity gas from an accreted object. (Abridged)Comment: To be published in the June 2000 issue of the Astronomical Journal. 28 pages, 13 figures, uses emulateap

Eddy diffusivity derived from drifter data for dispersion model applications

Ocean transport and dispersion processes are at the present time simulated using Lagrangian stochastic models coupled with Eulerian circulation models that are supplying analyses and forecasts of the ocean currents at unprecedented time and space resolution. Using the Lagrangian approach, each particle displacement is described by an average motion and a fluctuating part. The first one represents the advection associated with the Eulerian current field of the circulation models while the second one describes the sub-grid scale diffusion. The focus of this study is to quantify the sub-grid scale diffusion of the Lagrangian models written in terms of a horizontal eddy diffusivity. Using a large database of drifters released in different regions of the Mediterranean Sea, the Lagrangian sub-grid scale diffusion has been computed, by considering different regimes when averaging statistical quantities. In addition, the real drifters have been simulated using a trajectory model forced by OGCM currents, focusing on how the Lagrangian properties are reproduced by the simulated trajectories

Fused braids and centralisers of tensor representations of Uq(glN)U_q(gl_N)

We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and its deformation is defined on a set of topological objects that we call fused braids. We use these algebras to prove a Schur--Weyl duality theorem for any tensor products of any symmetrised powers of the natural representation of $U_q(gl_N)$. Then we proceed to the study of the fused Hecke algebras and in particular, we describe explicitely the irreducible representations and the branching rules. Finally, we aim to an algebraic description of the centralisers of the tensor products of $U_q(gl_N)$-representations under consideration. We exhibit a simple explicit element that we conjecture to generate the kernel from the fused Hecke algebra to the centraliser. We prove this conjecture in some cases and in particular, we obtain a description of the centraliser of any tensor products of any finite-dimensional representations of $U_q(sl_2)$.Comment: 52 page

Variational assimilation of Lagrangian trajectories in the Mediterranean ocean Forecasting System

Abstract. A novel method for three-dimensional variational assimilation of Lagrangian data with a primitive-equation ocean model is proposed. The assimilation scheme was implemented in the Mediterranean ocean Forecasting System and evaluated for a 4-month period. Four experiments were designed to assess the impact of trajectory assimilation on the model output, i.e. the sea-surface height, velocity, temperature and salinity fields. It was found from the drifter and Argo trajectory assimilation experiment that the forecast skill of surface-drifter trajectories improved by 15 %, that of intermediate-depth float trajectories by 20 %, and moreover, that the forecasted sea-surface height fields improved locally by 5 % compared to satellite data, while the quality of the temperature and salinity fields remained at previous levels. In conclusion, the addition of Lagrangian trajectory assimilation proved to reduce the uncertainties in the model fields, thus yielding a higher accuracy of the ocean forecasts

Optically variable active galactic nuclei in the 3 yr VST survey of the COSMOS field

The analysis of the variability of active galactic nuclei (AGNs) at different wavelengths and the study of possible correlations among different spectral windows are nowadays a major field of inquiry. Optical variability has been largely used to identify AGNs in multivisit surveys. The strength of a selection based on optical variability lies in the chance to analyze data from surveys of large sky areas by ground-based telescopes. However the effectiveness of optical variability selection, with respect to other multiwavelength techniques, has been poorly studied down to the depth expected from next generation surveys. Here we present the results of our r-band analysis of a sample of 299 optically variable AGN candidates in the VST survey of the COSMOS field, counting 54 visits spread over three observing seasons spanning > 3 yr. This dataset is > 3 times larger in size than the one presented in our previous analysis (De Cicco et al. 2015), and the observing baseline is ~8 times longer. We push towards deeper magnitudes (r(AB) ~23.5 mag) compared to past studies; we make wide use of ancillary multiwavelength catalogs in order to confirm the nature of our AGN candidates, and constrain the accuracy of the method based on spectroscopic and photometric diagnostics. We also perform tests aimed at assessing the relevance of dense sampling in view of future wide-field surveys. We demonstrate that the method allows the selection of high-purity (> 86%) samples. We take advantage of the longer observing baseline to achieve great improvement in the completeness of our sample with respect to X-ray and spectroscopically confirmed samples of AGNs (59%, vs. ~15% in our previous work), as well as in the completeness of unobscured and obscured AGNs. The effectiveness of the method confirms the importance to develop future, more refined techniques for the automated analysis of larger datasets.Comment: 21 pages, 10 figures; accepted for publication in A&

Kinematics of the Local Universe XIV. Measurements from the 21 cm line and the HI mass function from a homogeneous catalog gathered with the Nancay radio telescope

Aims. This paper presents 828 new 21 cm neutral hydrogen line measurements carried out with the FORT receiver of the meridian transit Nancay radio telescope (NRT) in the years 2000-2007.Methods. This observational program was part of a larger project aimed at collecting an exhaustive and magnitude-complete HI extragalactic catalog for Tully-Fisher applications. Through five massive data releases, the KLUN series has collected a homogeneous sample of 4876 HI-spectra of spiral galaxies, complete down to a flux of 5 Jy km s(-1) and with declination delta > -40 degreesResults. We publish here the last release of the KLUN HI observational program, corresponding to the faint end of the survey, with HI masses ranging from 5 x 10(8) to 5 x 10(10) solar masses. The size of this final sample is comparable to the catalogs based on the Arecibo and Parkes radio telescope campaigns, and it allows general HI mass distribution studies from a set of homogeneous radio measurements