2,131 research outputs found
The Lambda-structure Of The Representation Rings Of The Classical Weyl Groups
First, we introduce a class of operations, called {dollar}\phi{dollar}-operations, on the representation rings of the classical Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar}. These operations are shown to generate the exterior power operations in the representation rings {dollar}R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} and {dollar}R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})).{dollar} Given integers l, h satisfying {dollar}l + h=k{dollar}, let {dollar}\beta{dollar} be a partition of l and {dollar}\alpha{dollar} be a partition of h. The main theorem shows that induced representations of the form {dollar}{dollar}Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,\alpha{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1,{dollar}{dollar}where {dollar}{lcub}\cal W{rcub}\sb{lcub}B,a{rcub}=\prod{lcub}\cal W{rcub}(B\sb{lcub}B{rcub})\times\prod{lcub}\cal W{rcub}(A\sb{lcub}a{rcub}),{dollar} can be expressed as an algebraic combination of {dollar}\phi{dollar}-operations acting on the two canonical induced representations {dollar}{dollar}\eqalign{lcub}X\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub})\times{lcub}\cal W{rcub}(B\sb1){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\cr\cr Y\sb{lcub}k{rcub}&= Ind\sbsp{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k-1{rcub}){rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1.\cr{rcub}{dollar}{dollar};Next, we show that the set {dollar}{dollar}\left\{lcub}1 \otimes Ind\sbsp{lcub}{lcub}\cal W{rcub}\sb{lcub}\beta,a{rcub}{rcub}{lcub}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){rcub}1\right\{rcub}{dollar}{dollar}is a basis of {dollar}\doubq \otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar}. Since the {dollar}\phi{dollar}-operations generate the {dollar}\lambda{dollar}-operations, one can deduce that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(B\sb{lcub}k{rcub})){dollar} is generated as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar} by the elements {dollar}1 \otimes X\sb{lcub}k{rcub}{dollar} and {dollar}1 \otimes Y\sb{lcub}k{rcub}{dollar}. By applying a result of Lusztig which characterizes the irreducible representations of the Weyl groups {dollar}{lcub}\cal W{rcub}(B\sb{lcub}k{rcub}){dollar} and {dollar}{lcub}\cal W{rcub}(D\sb{lcub}k{rcub}){dollar} it follows, as a corollary, that {dollar}\doubq\otimes R({lcub}\cal W{rcub}(D\sb{lcub}k{rcub})){dollar} is generated by two elements as a {dollar}\lambda{dollar}-ring over {dollar}\doubq{dollar}
Star - Planet - Debris Disk Alignment in the HD 82943 system: Is planetary system coplanarity actually the norm?
Recent results suggest that the two planets in the HD 82943 system are
inclined to the sky plane by 20 +/- 4deg. Here, we show that the debris disk in
this system is inclined by 27 +/- 4deg, thus adding strength to the derived
planet inclinations and suggesting that the planets and debris disk are
consistent with being aligned at a level similar to the Solar System. Further,
the stellar equator is inferred to be inclined by 28 +/- 4deg, suggesting that
the entire star - planet - disk system is aligned, the first time such
alignment has been tested for radial velocity discovered planets on ~AU wide
orbits. We show that the planet-disk alignment is primordial, and not the
result of planetary secular perturbations to the disk inclination. In addition,
we note three other systems with planets at >10AU discovered by direct imaging
that already have good evidence of alignment, and suggest that empirical
evidence of system-wide star - planet - disk alignment is therefore emerging,
with the exception of systems that host hot Jupiters. While this alignment
needs to be tested in a larger number of systems, and is perhaps unsurprising,
it is a reminder that the system should be considered as a whole when
considering the orientation of planetary orbits.Comment: Accepted to MNRA
Huisgen-based conjugation of water-soluble porphyrins to deprotected sugars: Towards mild strategies for the labelling of glycans
Fully deprotected alkynyl-functionalised mono- and oligosaccharides undergo CuAAC-based conjugation with water-soluble porphyrin azides in aqueous environments. The mild reaction conditions are fully compatible with the presence of labile glycosidic bonds. This approach provides an ideal strategy to conjugate tetrapyrroles to complex carbohydrates
A Spitzer IRS Study of Debris Disks Around Planet-Host Stars
Since giant planets scatter planetesimals within a few tidal radii of their
orbits, the locations of existing planetesimal belts indicate regions where
giant planet formation failed in bygone protostellar disks. Infrared
observations of circumstellar dust produced by colliding planetesimals are
therefore powerful probes of the formation histories of known planets. Here we
present new Spitzer IRS spectrophotometry of 111 Solar-type stars, including
105 planet hosts. Our observations reveal 11 debris disks, including two
previously undetected debris disks orbiting HD 108874 and HD 130322. Combining
our 32 micron spectrophotometry with previously published MIPS photometry, we
find that the majority of debris disks around planet hosts have temperatures in
the range 60 < T < 100 K. Assuming a dust temperature T = 70 K, which is
representative of the nine debris disks detected by both IRS and MIPS, we find
that debris rings surrounding Sunlike stars orbit between 15 and 240 AU,
depending on the mean particle size. Our observations imply that the planets
detected by radial-velocity searches formed within 240 AU of their parent
stars. If any of the debris disks studied here have mostly large, blackbody
emitting grains, their companion giant planets must have formed in a narrow
region between the ice line and 15 AU.Comment: Accepted for publication in the Astronomical Journal. 14 pages,
including five figures and two table
Predicting the frequencies of diverse exo-planetary systems
Extrasolar planetary systems range from hot Jupiters out to icy comet belts
more distant than Pluto. We explain this diversity in a model where the mass of
solids in the primordial circumstellar disk dictates the outcome. The star
retains measures of the initial heavy-element (metal) abundance that can be
used to map solid masses onto outcomes, and the frequencies of all classes are
correctly predicted. The differing dependences on metallicity for forming
massive planets and low-mass cometary bodies are also explained. By
extrapolation, around two-thirds of stars have enough solids to form Earth-like
planets, and a high rate is supported by the first detections of low-mass
exo-planets.Comment: 5 pages, 2 figures; accepted by MNRA
The circumbinary disk of HD 98800B: Evidence for disk warping
The quadruple young stellar system HD 98800 consists of two spectroscopic binary pairs with a circumbinary disk around the B component. Recent work by Boden and collaborators using infrared interferometry and radial velocity data resulted in a determination of the physical orbit for HD 98800B. We use the resulting inclination of the binary and the measured extinction toward the B component stars to constrain the distribution of circumbinary material. Although a standard optically and geometrically thick disk model can reproduce the spectral energy distribution, it cannot account for the observed extinction if the binary and the disk are coplanar. We next constructed a dynamical model to investigate the influence of the A component, which is not in the Ba‐Bb orbital plane, on the B disk. We find that these interactions have a substantial impact on the inclination of the B circumbinary disk with respect to the Ba‐Bb orbital plane. The resulting warp would be sufficient to place material into the line of sight and the noncoplanar disk orientation may also cause the upper layers of the disk to intersect the line of sight if the disk is geometrically thick. These simulations also support that the dynamics of the Ba‐Bb orbit clear the inner region to a radius of~3 AU. We then discuss whether the somewhat unusual properties of the HD 98800B disk are consistent with material remnant from the star formation process or with more recent creation by collisions from larger bodies
Origin of the Mediterranean outflow
Toe origin of the Mediterranean outflow is one of oceanography\u27s oldest problems. In this work, the flow of western Mediterranean deep water up and over the sill at Gibraltar is investigated from hydrographic observations and current measurements. The deep water is found to flow westward along the Moroccan continental slope in the western Mediterranean or Alboran Sea and to rise as it approaches the Strait of Gibraltar...
- …