Two-Rowed Hecke Algebra Representations at Roots of Unity

In this paper, we initiate a study into the explicit construction of irreducible representations of the Hecke algebra $H_n(q)$ of type $A_{n-1}$ in the non-generic case where $q$ is a root of unity. The approach is via the Specht modules of $H_n(q)$ which are irreducible in the generic case, and possess a natural basis indexed by Young tableaux. The general framework in which the irreducible non-generic $H_n(q)$-modules are to be constructed is set up and, in particular, the full set of modules corresponding to two-part partitions is described. Plentiful examples are given.Comment: LaTeX, 9 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' Prague, 22-24 June 199

\u27Race, Racism, and American Law \u27: A Seminar From The Indigenous, Black, And Immigrant Legal Perspectives

The events of fall 2016 exploded the myth of a post-racial America that some believed had been ushered in by Barack Obama’s presidency.1With the U.S. presidential campaign in full swing, soon-to-be President Donald Trump disparaged Muslims as terrorists, Mexicans as rapists and murderers, and African Americans as poor.2 Trump’s racist demagoguery came amidst the momentum of the Black Lives Matter,Standing Rock, and Dreamer movements—mass mobilizations that sought to end the police killings of Black people, protect Native American treaty rights, and grant immigrant minors legal status.3 Once again, the racial divide that has defined this nation since its inception 2019] RACE,RACISM,ANDAMERICANLAW 3reemerged in the national discourse with an intensity that exposed the fallacy of post-racialism.4The national anger, confusion, and vulnerability sown by that fall’s campaign reflected and reverberated in our community in Montana. They fractured our law school, our university, our state, and our city along lines of difference, not the least of which was racial.5 We would not know until November that Trump would be elected president. We would not know until after his inauguration that he would harden and intensify his racist agenda.6 But we sensed a new era had dawned, and therefore, we and our students needed to understand the undercurrents and urgencies of the moment. In response, we sought to reaffirm an anti-racist agenda and harness the ferment by finding common ground in the legal treatments of Native Americans, African Americans, and immigrants. That is how our seminar, “Race, Racism, and American Law from the Native American, African American, and Immigrant Legal Perspectives,” came to be

Antiracism, Reflection, and Professional Identity

Intent on more systematically developing the emerging professional identities of law students, the professional identity formation movement is recasting how we think about legal education. Notably, however, the movement overlooks the structural racism imbedded in American law and legal education. While current models of professional development value diversity and cross-cultural competence, they do not adequately prepare the next generation of legal professionals to engage in the sustained work of interrupting and overthrowing race and racism in the legal profession and system. This article argues that antiracism is essential to the profession’s responsibility to serve justice and therefore key to legal professional identity. Fortunately, developing a legal antiracist identity does not require inventing a new approach. Rather, infusing reflective practice with critical race consciousness provides a sound basis from which to launch a new effort to develop the next generation of antiracist lawyers

Antiracism, Reflection, and Professional Identity

Intent on more systematically developing the emerging professional identities of law students, the professional identity formation movement is recasting how we think about legal education. Notably, however, the movement overlooks the structural racism imbedded in American law and legal education. While current models of professional development value diversity and cross-cultural competence, they do not adequately prepare the next generation of legal professionals to engage in the sustained work of interrupting and overthrowing race and racism in the legal profession and system. This article argues that antiracism is essential to the profession’s responsibility to serve justice and therefore key to legal professional identity. Fortunately, developing a legal antiracist identity does not require inventing a new approach. Rather, infusing reflective practice with critical race consciousness provides a sound basis from which to launch a new effort to develop the next generation of antiracist lawyers

Parafermionic algebras, their modules and cohomologies

We explore the Fock spaces of the parafermionic algebra introduced by H.S. Green. Each parafermionic Fock space allows for a free minimal resolution by graded modules of the graded 2-step nilpotent subalgebra of the parafermionic creation operators. Such a free resolution is constructed with the help of a classical Kostant's theorem computing Lie algebra cohomologies of the nilpotent subalgebra with values in the parafermionic Fock space. The Euler-Poincar\'e characteristics of the parafermionic Fock space free resolution yields some interesting identities between Schur polynomials. Finally we briefly comment on parabosonic and general parastatistics Fock spaces.Comment: 10 pages, talk presented at the International Workshop "Lie theory and its applications in Physics" (17-23 June 2013, Varna, Bulgaria

The \u27Second Wave\u27 of Spanish Clinical Legal Education: Empirical, Pedagogical, and Institutional Lessons for a Pilot Course and Program at the University of Granada

Spanish clinicians today benefit from the ‘first wave’ of early adopters. We also benefit from decades of clinical scholarship—most recently about the Western European and global clinical legal education movements—and empirical data on what lawyers actually do and need in practice. In this article, the authors summarize key empirical, pedagogical, and institutional lessons to ground the creation of a pilot course and program at the University of Granada

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

Controlling the structures of organic semiconductor–quantum dot nanocomposites through ligand shell chemistry

Nanocrystal quantum dots (QD) functionalised with active organic ligands hold significant promise as solar energy conversion materials, capable of multiexcitonic processes that could improve the efficiencies of single-junction photovoltaic devices. Small-angle X-ray and neutron scattering (SAXS and SANS) were used to characterize the structure of lead sulphide QDs post ligand-exchange with model acene-carboxylic acid ligands (benzoic acid, hydrocinnamic acid and naphthoic acid). Results demonstrate that hydrocinnamic acid and naphthoic acid ligated QDs form monolayer ligand shells, whilst benzoic acid ligated QDs possess ligand shells thicker than a monolayer. Further, the formation of a range of nanocomposite materials through the self-assembly of such acene-ligated QDs with an organic small-molecule semiconductor [5,12-bis((triisopropylsilyl)ethynyl)tetracene (TIPS-Tc)] is investigated. These materials are representative of a wider set of functional solar energy materials; here the focus is on structural studies, and their optoelectronic function is not investigated. As TIPS-Tc concentrations are increased, approaching the solubility limit, SANS data show that QD fractal-like features form, with structures possibly consistent with a diffusion limited aggregation mechanism. These, it is likely, act as heterogeneous nucleation agents for TIPS-Tc crystallization, generating agglomerates containing both QDs and TIPS-Tc. Within the TIPS-Tc crystals there seem to be three distinct QD morphologies: (i) at the crystallite centre (fractal-like QD aggregates acting as nucleating agents), (ii) trapped within the growing crystallite (giving rise to QD features ordered as sticky hard spheres), and (iii) a population of aggregate QDs at the periphery of the crystalline interface that were expelled from the growing TIPS-Tc crystal. Exposure of the QD:TIPS-Tc crystals to DMF vapour, a solvent known to be able to strip ligands from QDs, alters the spacing between PbS–hydrocinnamic acid and PbS–naphthoic acid ligated QD aggregate features. In contrast, for PbS–benzoic acid ligated QDs, DMF vapour exposure promotes the formation of ordered QD colloidal crystal type phases. This work thus demonstrates how different QD ligand chemistries control the interactions between QDs and an organic small molecule, leading to widely differing self-assembly processes. It highlights the unique capabilities of multiscale X-ray and neutron scattering in characterising such composite materials

American Society of Hematology 2020 guidelines for sickle cell disease: Prevention, diagnosis, and treatment of cerebrovascular disease in children and adults

BACKGROUND: Central nervous system (CNS) complications are among the most common, devastating sequelae of sickle cell disease (SCD) occurring throughout the lifespan.OBJECTIVE: These evidence-based guidelines of the American Society of Hematology are intended to support the SCD community in decisions about prevention, diagnosis, and treatment of the most common neurological morbidities in SCD.METHODS: The Mayo Evidence-Based Practice Research Program supported the guideline development process, including updating or performing systematic evidence reviews. The panel used the Grading of Recommendations Assessment, Development and Evaluation (GRADE) approach, including GRADE evidence-to-decision frameworks, to assess evidence and make recommendations.RESULTS: The panel placed a higher value on maintaining cognitive function than on being alive with significantly less than baseline cognitive function. The panel developed 19 recommendations with evidence-based strategies to prevent, diagnose, and treat CNS complications of SCD in low-middle- and high-income settings.CONCLUSIONS: Three of 19 recommendations immediately impact clinical care. These recommendations include: use of transcranial Doppler ultrasound screening and hydroxyurea for primary stroke prevention in children with hemoglobin SS (HbSS) and hemoglobin Sβ0 (HbSβ0) thalassemia living in low-middle-income settings; surveillance for developmental delay, cognitive impairments, and neurodevelopmental disorders in children; and use of magnetic resonance imaging of the brain without sedation to detect silent cerebral infarcts at least once in early-school-age children and once in adults with HbSS or HbSβ0 thalassemia. Individuals with SCD, their family members, and clinicians should become aware of and implement these recommendations to reduce the burden of CNS complications in children and adults with SCD.</p

A mutli-technique search for the most primitive CO chondrites

As part of a study to identify the most primitive COs and to look for weakly altered CMs amongst the COs, we have conducted a multi-technique study of 16 Antarctic meteorites that had been classified as primitive COs. For this study, we have determined: (1) the bulk H, C and N abundances and isotopes, (2) bulk O isotopic compositions, (3) bulk modal mineralogies, and (4) for some selected samples the abundances and compositions of their insoluble organic matter (IOM). Two of the 16 meteorites do appear to be CMs – BUC 10943 seems to be a fairly typical CM, while MIL 090073 has probably been heated. Of the COs, DOM 08006 appears to be the most primitive CO identified to date and is quite distinct from the other members of its pairing group. The other COs fall into two groups that are less primitive than DOM 08006 and ALH 77307, the previously most primitive CO. The first group is composed of members of the DOM 08004 pairing group, except DOM 08006. The second group is composed of meteorites belonging to the MIL 03377 and MIL 07099 pairing groups. These two pairing groups should probably be combined. There is a dichotomy in the bulk O isotopes between the primitive (all Antarctic finds) and the more metamorphosed COs (mostly falls). This dichotomy can only partly be explained by the terrestrial weathering experienced by the primitive Antarctic samples. It seems that the more equilibrated samples interacted to a greater extent with 16O-poor material, probably water, than the more primitive meteorites