Center and representations of infinitesimal Hecke algebras of sl_2

In this paper, we compute the center of the infinitesimal Hecke algebras Hz associated to sl_2 ; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category O. We also discuss central elements in infinitesimal Hecke algebras over gl(n) and sp(2n) for all n. We end by proving an analogue of the theorem of Duflo for Hz.Comment: Final form, to appear in "Communications in Algebra"; 35 pages, laTe

The Distribution of Dark Matter in a Ringed Galaxy

Outer rings are located at the greatest distance from the galaxy center of any feature resonant with a bar. Because of their large scale, their morphology is sensitive to the distribution of the dark matter in the galaxy. We introduce here how study of these rings can constrain the mass-to-light ratio of the bar, and so the percentage of dark matter in the center of these galaxies. We compare periodic orbits integrated in the ringed galaxy NGC 6782 near the outer Lindblad resonance to the shape of the outer ring. The non-axisymmetric component of the potential resulting from the bar is derived from a near-infrared image of the galaxy. The axisymmetric component is derived assuming a flat rotation curve. We find that the pinched non-self-intersecting periodic orbits are more elongated for higher bar mass-to-light ratios and faster bars. The inferred mass-to-light ratio of the bar depends on the assumed inclination of the galaxy. With an assumed galaxy inclination of i=41 degrees, for the orbits to be consistent with the observed ring morphology the mass-to-light ratio of the bar must be high, greater than 70% of a maximal disk value. For i=45 degrees, the mass-to-light ratio of the bar is $75\pm 15$ of the maximal disk value. Since the velocity field of these rings can be used to constrain the galaxy inclination as well as which periodic orbit is represented in the ring, further study will yield tighter constraints on the mass-to-light ratio of the bar. If a near maximal disk value for the bar is required, then either there would be little dark matter within the bar, or the dark matter contained in the disk of the galaxy would be non-axisymmetric and would rotate with the bar.Comment: AAS Latex + jpg Figures, Accepted for publication in Ap

Toric rings, inseparability and rigidity

This article provides the basic algebraic background on infinitesimal deformations and presents the proof of the well-known fact that the non-trivial infinitesimal deformations of a $K$-algebra $R$ are parameterized by the elements of cotangent module $T^1(R)$ of $R$. In this article we focus on deformations of toric rings, and give an explicit description of $T^1(R)$ in the case that $R$ is a toric ring. In particular, we are interested in unobstructed deformations which preserve the toric structure. Such deformations we call separations. Toric rings which do not admit any separation are called inseparable. We apply the theory to the edge ring of a finite graph. The coordinate ring of a convex polyomino may be viewed as the edge ring of a special class of bipartite graphs. It is shown that the coordinate ring of any convex polyomino is inseparable. We introduce the concept of semi-rigidity, and give a combinatorial description of the graphs whose edge ring is semi-rigid. The results are applied to show that for $m-k=k=3$, $G_{k,m-k}$ is not rigid while for $m-k\geq k\geq 4$, $G_{k,m-k}$ is rigid. Here $G_{k,m-k}$ is the complete bipartite graph $K_{m-k,k}$ with one edge removed.Comment: 33 pages, chapter 2 of the Book << Multigraded Algebra and Applications>> 2018, Springer International Publishing AG, part of Springer Natur

Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a compact Lie group and the Chern character is explicitly computed in the case of SU(2). For large euclidean time, the character form is localized on a D-brane.Comment: Version 2: Essentially simplified proof of the main result using a map from twisted K-theory to gerbes modulo the twisting gerbe; references added + minor correction

Sex and Gender Topics in Medical Student Learners: Follow up

TOP WINNER Background: In an era of patient-centered, individualized medicine, it is important to consider of the impact of sex and gender on mechanisms of health and disease. Objectives: This study aimed to assess medical students’ current knowledge of sex and gender-based medical concepts and to compare responses to the prior assessment at Mayo Clinic in order to better inform ongoing efforts to improve medical education curricular materials. Methods: An electronic survey that assessed current knowledge of sex and genderbased medicine was sent to all 1st – 4th year medical students at the Mayo Clinic Minnesota and Arizona campuses. Descriptive and qualitative thematic results were compared to the same survey administered in 2012 to assess the efficacy of curriculum changes in better covering sex and gender-based medicine topics. Results: A total of 100 of 365 (27% response rate) of students responded, with 2:1 female to male with representation from all 4 years. The terms sex and gender were correctly identified by most respondents (93%). Various medical knowledge questions were answered incorrectly. Students reported many areas where concepts of sex and gender were not routinely covered n including orthopedics and nephrology, although these percentages have increased since 2012. Sixty two percent of students favored increasing sex and gender health concepts in the current curriculum. Conclusions: Medical students appear to understand the definition of and importance of sex and gender. While some improvements in coverage by topic area have occurred, opportunity remains to more fully integrate these concepts in medical school curricula.https://jdc.jefferson.edu/sexandgenderhealth/1023/thumbnail.jp

Manin products, Koszul duality, Loday algebras and Deligne conjecture

In this article we give a conceptual definition of Manin products in any category endowed with two coherent monoidal products. This construction can be applied to associative algebras, non-symmetric operads, operads, colored operads, and properads presented by generators and relations. These two products, called black and white, are dual to each other under Koszul duality functor. We study their properties and compute several examples of black and white products for operads. These products allow us to define natural operations on the chain complex defining cohomology theories. With these operations, we are able to prove that Deligne's conjecture holds for a general class of operads and is not specific to the case of associative algebras. Finally, we prove generalized versions of a few conjectures raised by M. Aguiar and J.-L. Loday related to the Koszul property of operads defined by black products. These operads provide infinitely many examples for this generalized Deligne's conjecture.Comment: Final version, a few references adde

Systematic motions in the Galactic plane found in the Hipparcos Catalogue using Herschel's Method

Two motions in the galactic plane have been detected and characterized, based on the determination of a common systematic component in Hipparcos catalogue proper motions. The procedure is based only on positions, proper motions and parallaxes, plus a special algorithm which is able to reveal systematic trends. Our results come from two stellar samples. Sample 1 has 4566 stars and defines a motion of apex (l,b)=(177.8,3.7)+/-(1.5,1.0) and space velocity V=27+/-1 km/s. Sample 2 has 4083 stars and defines a motion of apex (l,b)=(5.4,-0.6)+/-(1.9,1.1) and space velocity V=32+/-2 km/s. Both groups are distributed all over the sky and cover a large variety of spectral types, which means that they do not belong to a specific stellar population. Herschel's method is used to define the initial samples of stars and later to compute the common space velocity. The intermediate process is based on the use of a special algorithm to determine systematic components in the proper motions. As an important contribution, this paper sets out a new way to study the kinematics of the solar neighborhood, in the search for streams, associations, clusters and any other space motion shared by a large number of stars, without being restricted by the availability of radial velocities.Comment: 12 pages and 12 eps figures. LaTe

Disentangling the circumnuclear environs of Centaurus A: II. On the nature of the broad absorption line

We report on atomic gas (HI) and molecular gas (as traced by CO(2-1)) redshifted absorption features toward the nuclear regions of the closest powerful radio galaxy, Centaurus A (NGC 5128). Our HI observations using the Very Long Baseline Array allow us to discern with unprecedented sub-parsec resolution HI absorption profiles toward different positions along the 21 cm continuum jet emission in the inner 0."3 (or 5.4 pc). In addition, our CO(2-1) data obtained with the Submillimeter Array probe the bulk of the absorbing molecular gas with little contamination by emission, not possible with previous CO single-dish observations. We shed light with these data on the physical properties of the gas in the line of sight, emphasizing the still open debate about the nature of the gas that produces the broad absorption line (~55 km/s). First, the broad H I line is more prominent toward the central and brightest 21 cm continuum component than toward a region along the jet at a distance ~ 20 mas (or 0.4 pc) further from it. This suggests that the broad absorption line arises from gas located close to the nucleus, rather than from diffuse and more distant gas. Second, the different velocity components detected in the CO(2-1) absorption spectrum match well other molecular lines, such as those of HCO+(1-0), except the broad absorption line that is detected in HCO+(1-0) (and most likely related to that of the H I). Dissociation of molecular hydrogen due to the AGN seems to be efficient at distances <= 10 pc, which might contribute to the depth of the broad H I and molecular lines.Comment: 17 pages, 9 figures, accepted for publication in Ap