4,657 research outputs found
Highest weight modules and polarized embeddings of shadow spaces
Let Gamma be the K-shadow space of a spherical building Delta. An embedding V
of Gamma is called polarized if it affords all "singular" hyperplanes of Gamma.
Suppose that Delta is associated to a Chevalley group G. Then Gamma can be
embedded into what we call the Weyl module for G of highest weight lambda_K. It
is proved that this module is polarized and that the associated minimal
polarized embedding is precisely the irreducible G-module of highest weight
lambda_K. In addition a number of general results on polarized embeddings of
shadow spaces are proved. The last few sections are devoted to the study of
specific shadow spaces, notably minuscule weight geometries, polar
grassmannians, and projective flag-grassmannians. The paper is in part
expository in nature so as to make this material accessible to a wide audience.Comment: Improvement in exposition of Sections 1-3 and . Notation improved.
References added. Main results unchange
Halo Mass Profiles and Low Surface Brightness Galaxies Rotation Curves
A recent study has claimed that the rotation curve shapes and mass densities
of Low Surface Brightness (LSB) galaxies are largely consistent with
CDM predictions, in contrast to a large body of observational work. I
demonstrate that the method used to derive this conclusion is incapable of
distinguishing the characteristic steep CDM mass-density distribution from the
core-dominated mass-density distributions found observationally: even
core-dominated pseudo-isothermal haloes would be inferred to be consistent with
CDM. This method can therefore make no definitive statements on the
(dis)agreement between the data and CDM simulations. After introducing an
additional criterion that does take the slope of the mass-distribution into
account I find that only about a quarter of the LSB galaxies investigated are
possibly consistent with CDM. However, for most of these the fit parameters are
so weakly constrained that this is not a strong conclusion. Only 3 out of 52
galaxies have tightly constrained solutions consistent with CDM. Two
of these galaxies are likely dominated by stars, leaving only one possible dark
matter dominated, CDM-consistent candidate, forming a mere 2 per cent of the
total sample. These conclusions are based on comparison of data and simulations
at identical radii and fits to the entire rotation curves. LSB galaxies that
are consistent with CDM simulations, if they exist, seem to be rare indeed.Comment: Accepted for publication in Astrophysical Journa
The First CO Map of a Low Surface Brightness Galaxy
Using the Owens Valley Radio Observatory Millimeter-Wavelength Array (OVRO)
we have obtained the first CO map of a low surface brightness (LSB) galaxy. The
studied galaxy, UGC 01922, was chosen for these observations because both of
its previous CO detection with the IRAM 30m telescope and its classification as
a Malin 1 `cousin' - an LSB galaxy with M_HI > 10^10 Msol. The OVRO map
detected approximately 65% of the CO(1-0) flux found earlier with the single
dish measurements, giving a detected gas mass equivalent to M_H2 = 1.1X10^9
Msol. The integrated gas peak lies at the center of the galaxy and coincides
with both the optical and 1.4 GHz continuum emission peaks. The molecular gas
extends well beyond the OVRO beam size (~4'' or 3 kpc), covering ~25% of the
optical bulge. In all, perhaps the most remarkable aspect of this map is its
unexceptional appearance. Given that it took over ten years to successfully
detect molecular gas in any low surface brightness system, it is surprising
that the appearance and distribution of UGC 01922's CO is similar to what would
be expected for a high surface brightness galaxy in the same morphological
class.Comment: 5 pages, including 3 figures and 3 tables. also available online at
http://www.gb.nrao.edu/~koneil. Accepted by ApJ
Two-body hadronic charmed meson decays
We study in this work the two-body hadronic charmed meson decays, including
both the PP and VP modes. The latest experimental data are first analyzed in
the diagrammatic approach. The magnitudes and strong phases of the flavor
amplitudes are extracted from the Cabibbo-favored (CF) decay modes using
minimization. The best-fitted values are then used to predict the
branching fractions of the singly-Cabibbo-suppressed (SCS) and
doubly-Cabibbo-suppressed decay modes in the flavor SU(3) symmetry limit. We
observe significant SU(3) breaking effects in some of SCS channels. In the case
of VP modes, we point out that the and amplitudes cannot be
completely determined based on currently available data. We conjecture that the
quoted experimental results for both and are overestimated. We compare the sizes of color-allowed and
color-suppressed tree amplitudes extracted from the diagrammatical approach
with the effective parameters and defined in the factorization
approach. The ratio is more or less universal among the , and modes. This feature allows
us to discriminate between different solutions of topological amplitudes. For
the long-standing puzzle about the ratio , we argue that, in addition to the SU(3)
breaking effect in the spectator amplitudes, the long-distance resonant
contribution through the nearby resonance can naturally explain why
decays more copiously to than through the
-exchange topology.Comment: 32 pages, 5 figures. An alternative method for error bar extraction
is used; last columns of Tables~I to VI, and all entries in Tables~VII, VIII
and X are modified. To appear in PRD
The generating rank of the unitary and symplectic Grassmannians
We prove that the Grassmannian of totally isotropic -spaces of the polar
space associated to the unitary group () has generating rank when . We also reprove the main result of Blok [Blok2007], namely that
the Grassmannian of totally isotropic -spaces associated to the symplectic
group has generating rank , when
Further Discoveries of 12CO in Low Surface Brightness Galaxies
Using the IRAM 30m telescope we have obtained seven new, deep CO J(1-0) and
J(2-1) observations of low surface brightness (LSB) galaxies. Five of the
galaxies have no CO detected to extremely low limits (0.1-0.4 K km/s at
J(1-0)), while two of the galaxies, UGC 01922 and UGC 12289, have clear
detections in both line transitions. When these observations are combined with
all previous CO observations taken of LSB systems, we compile a total of 34
observations, in which only 3 galaxies have had detections of their molecular
gas. Comparing the LSB galaxies with and without CO detections to a sample of
high surface brightness (HSB) galaxies with CO observations indicates that it
is primarily the low density of baryonic matter within LSB galaxies which is
causing their low CO fluxes. Finally, we note that one of the massive LSB
galaxies studied in this project, UGC 06968 (a Malin-1 `cousin'), has upper
limits placed on both M_H2 and M_H2/M_HI which are 10-20 times lower than the
lowest values found for any galaxy (LSB or HSB) with similar global properties.
This may be due to an extremely low temperature and metallicity within UGC
06968, or simply due to the CO distribution within the galaxy being too diffuse
to be detected by the IRAM beam.Comment: 18 pages, 8 figures, 4 tables. Accepted by Ap
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