K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where G = GL(n,\C), and where $K$ is one of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit closures as universal degeneracy loci for a vector bundle over a variety equipped with a single flag of subbundles and a nondegenerate symmetric or skew-symmetric bilinear form taking values in the trivial bundle. We describe how our equivariant formulas can be interpreted as giving formulas for the classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version, to appear in Transformation Group

Community Change within a Caribbean Coral Reef Marine Protected Area following Two Decades of Local Management

Structural change in both the habitat and reef-associated fish assemblages within spatially managed coral reefs can provide key insights into the benefits and limitations of Marine Protected Areas (MPAs). While MPA zoning effects on particular target species are well reported, we are yet to fully resolve the various affects of spatial management on the structure of coral reef communities over decadal time scales. Here, we document mixed affects of MPA zoning on fish density, biomass and species richness over the 21 years since establishment of the Saba Marine Park (SMP). Although we found significantly greater biomass and species richness of reef-associated fishes within shallow habitats (5 meters depth) closed to fishing, this did not hold for deeper (15 m) habitats, and there was a widespread decline (38% decrease) in live hard coral cover and a 68% loss of carnivorous reef fishes across all zones of the SMP from the 1990s to 2008. Given the importance of live coral for the maintenance and replenishment of reef fishes, and the likely role of chronic disturbance in driving coral decline across the region, we explore how local spatial management can help protect coral reef ecosystems within the context of large-scale environmental pressures and disturbances outside the purview of local MPA management.Funding was provided by the Saba Conservation Foundation ((SCF), King Abdullah University of Science and Technology, The Australian National University and Australian Research Council. The funders had no role in study design and analysis, decision to publish, or preparation of the manuscript. Staff of the SCF were involved in data collection

Enantioselective Total Synthesis of (–)-Myrifabral A and B

A catalytic enantioselective approach to the Myrioneuron alkaloids (−)-myrifabral A and (−)-myrifabral B is described. The synthesis was enabled by a palladium-catalyzed enantioselective allylic alkylation, that generates the C(10) all-carbon quaternary center. A key N-acyl iminium ion cyclization forged the cyclohexane fused tricyclic core, while vinyl boronate cross metathesis and oxidation afforded the lactol ring of (−)-myrifabral A. Adaptation of previously reported conditions allowed for the conversion of (−)-myrifabral A to (−)-myrifabral B

Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.Comment: 43 pages, uses harvmac,version 2 2 references added, minor typos correcte

On the integral cohomology of smooth toric varieties

Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In some cases we can also give the product. As a corollary we obtain that the cycle map from Chow groups to integral Borel-Moore homology is split injective for smooth toric varieties. Another result is that the differential algebra of singular cochains on the Borel construction of $X_\Sigma$ is formal.Comment: 10 page

Higher su(N) tensor products

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.Comment: 17 pages, LaTe

Moduli Spaces of Lumps on Real Projective Space

Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge three lumps is a D2-symmetric 7-dimensional manifold of cohomogeneity one. In this paper, we discuss the charge three moduli spaces of lumps from two perspectives: discrete symmetries of lumps and the Riemann-Hurwitz formula. We then calculate the metric and find explicit formula for various geometric quantities. We also discuss the implications for lump decay

The Cordilleran Ice Sheet and the Glacial Geomorphology of Southern and Central British Colombia

This paper reviews the current state of knowledge about the Cordilleran Ice Sheet in southern and central British Columbia. Reconstructions of the ice sheet and the styles of ice expansion and déglaciation are based on extensive and varied glacigenic sediments and landforms that date from Late Wisconsinan (Fraser) Glaciation. Late-glacial lakes and sea level changes are also described and related to isostatic and eustatic effects. The timing of ice expansion and recession during Fraser Glaciation was markedly asymmetric: ice build-up commenced about 29 000 years BP, culminated between 14 500 and 14 000 years BP1 and déglaciation was largely completed by 11 500 years BP. Most of this interval appears to have been dominated by montane glaciation, which produced striking erosional landforms. A Cordilleran Ice Sheet existed from only about 19 000 to 13 500 years BP. An older glaciation, probably of Early Wisconsinan age, has been recognized from widespread exposures of drift that underlies Middle Wisconsinan non-glacial sediments. Pre-Wisconsinan drift is present near Vancouver. Drifts of late Tertiary to Middle Pleistocene age have been dated by association with volcanic sequences in the southern Coast Mountains and the central Interior, and by paleomagnetic studies in the southern Interior.On résume ici l'état des connaissances sur l'Inlandsis de la Cordillère du sud et du centre de la Colombie-Britannique. Les reconstitutions de l'inlandsis et les modes d'englaciation et de déglaciation sont fondés sur les formes et les sédiments glaciaires qui datent de la glaciation du Wisconsinien supérieur (Fraser). On décrit également les lacs tardiglaciaires et les changements du niveau marin en relation avec les conséquences sur les niveaux isostatique et eustatique. Les rythmes de la progression et du retrait glaciaire ont été tout à fait différents; la giaciation a commencé vers 29 000 BP, a connu son optimum entre 14 500 et 14 000 BP et la déglaciation était à toutes fins utiles terminée dès 11 500 BP. La plus grande partie de cette époque a été dominée par une glaciation de type alpin, qui a engendré des formes d'érosion remarquables. L'Inlandsis de la Cordillère n'a existé que de 19 000 à 13 500 BP. On a identifié une glaciation plus ancienne, probablement du Wisconsinien inférieur, à partir des affleurements répandus de dépôts glaciaires sous-jacents aux sédiments non glaciaires du Wisconsinien moyen. On a observé des dépôts glaciaires pré-wisconsiniens près de Vancouver. Les dépôts glaciaires datant du Tertiaire supérieur au Pleistocene moyen ont été datés par association aux séquences volcaniques du sud des montagnes Côtières et du centre de l'Intérieur et grâce à des études de paléomagnétisme menées dans le sud du système de l'Intérieur.Dieser Artikel gibt einen uberblick ûber den gegenwartigen Forschungsstand zur Kordilleren-Eisdecke im Sùden und im Zentrum von British Columbia. Die Rekonstruktionen der Eisdecke und der Art und Weise der Eisausdehnung und Enteisung stùtzen sich auf extensive und mannigfache glazigene Sedimente und Landformen, die aus der Spât-Wisconsin- (Fraser) Vereisung stammen. Spàtglaziale Seen und Meeresniveauwechsel werden auch beschrieben und in Beziehung zu isostatischen und eustatischen Auswirkungen gesetzt. Der zeitliche Ablauf der Eisausdehnung und des Eisrùckzugs wàhrend der Fraser-Vereisung war deutlich asymmetrisch : die Vereisung begann um etwa 29 000 Jahre v.u.Z., erreichte ihren Hôchststand zwischen 14 500 und 14 000 Jahren v.u.Z. und die Enteisung war weitgehend vollendet um 11 500 Jahre v.u.Z. Der grôfîte Tail dieses Zeitraums scheint von einer alpinen Vereisung beherrscht gewesen zu sein, welche eindrucksvolle Erosions-Landformen hervorbrachte. Eine Kordilleren-Eisdecke existierte nur von etwa 19 000 bis 13 500 Jahre v.u.Z. Eine altère Vereisung, môglicherweise aus dem frùhen Wisconsin konnte anhand ausgedehnter Anlagen von glazialen Ablagerungen, die sich unter nichtglazialen Sedimenten des mittleren Wiskonsin befinden, identifiziert werden. Abgelagerte Bildungen aus dem Spàttertiâr bis zum mittleren Pleistozân wurden in Verbindung mit vulkanischen Sequenzen in den Bergen der Sùdkùste und dem zentralen Landesinnern und mittels palàomagnetischen Studien im sûdlichen Landesinnern datiert

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions