Extensions, Levi subgroups and character formulas

This paper consists of three interconnected parts. Parts I,III study the relationship between the cohomology of a reductive group and that of a Levi subgroup. For example, we provide a necessary condition, arising from Kazhdan-Lusztig theory, for the natural map on Ext-groups of irreducible modules to be surjective. In cohomological degree 1, the map is always an isomorphism, under our hypothesis. These results were inspired by recent work of Hemmer obtained for general linear groups, and they both extend and improve upon his work when our condition is met. Part II obtains results on Lusztig character formulas for reductive groups, obtaining new necessary and sufficient conditions for such formulas to hold. In the special case of general linear groups, these conditions can be recast in a striking way completely in terms of explicit representation theoretic properties of the symmetric group (and the results improve upon the sufficient cohomological conditions established recently in the authors)

Recovering a Lost Story Using Oral History: The United States Supreme Court\u27s Historic Green v. New Kent County, Virginia, Decision

In 1965, New Kent County, located just east of Richmond, Virginia, became the setting for the one of the most important school desegregation cases since Brown v. Board of Education. Ten years after the U.S. Supreme Court declared separate but equal unconstitutional, both public schools in New Kent, the George W. Watkins School for blacks and the New Kent School for whites, remained segregated. In 1965, however, local blacks and the Virginia State NAACP initiated a legal challenge to segregated schools, hoping to initiate desegregation where the process had yet to begin and to accelerate the process in areas where token desegregation was the norm. In 1968, the U.S. Supreme Court decision inCharles C. Green v. the School Board of New Kent County forced New Kent County and localities across the state and nation to fulfill the promise of Brown. While the case has been part of the court records since it was decided in 1968, it has remained largely unknown to the general public and many scholars of the era. This article is an attempt to use the tool of oral history to present the people and the story behind Green v. New Kent County and to add another piece to the puzzle that was school desegregation in this country

Evolution of 4 pi observables in the Vlasov-Uehling-Uhlenbeck theory and the transverse momentum transfer as a barometer for hadronic matter

We study the dynamics of high energy heavy ion collisions through the Vlasov-Uehling-Uhlenbeck approach. Equilibration is observed, for central collisions. It is shown that the produced entropy, the pion multiplicity, flow angle, and transverse momentum distributions saturate at the moment of maximum compression and temperature. The effects of the nuclear equation of state and the Pauli principle are investigated. For the flow angle distribution there is a 20 deg reduction of the peak flow angle due to the Pauli principle. A stiff equation of state results in a 10–20 deg increase over the soft equation of state at all energies. The transverse momentum at projectile rapidity exhibits a peak structure as a function of impact parameter b. A 40% difference between soft and hard equation of state is observed for the peak impact parameter, i.e., for intermediate multiplicities

Asp-120 Locates Zn2 for Optimal Metallo-β-lactamase Activity

Metallo-β-lactamases are zinc-dependent hydrolases that inactivate β-lactam antibiotics, rendering bacteria resistant to them. Asp-120 is fully conserved in all metallo-β-lactamases and is central to catalysis. Several roles have been proposed for Asp-120, but so far there is no agreed consensus. We generated four site-specifically substituted variants of the enzyme BcII from Bacillus cereus as follows: D120N, D120E, D120Q, and D120S. Replacement of Asp-120 by other residues with very different metal ligating capabilities severely impairs the lactamase activity without abolishing metal binding to the mutated site. A kinetic study of these mutants indicates that Asp-120 is not the proton donor, nor does it play an essential role in nucleophilic activation. Spectroscopic and crystallographic analysis of D120S BcII, the least active mutant bearing the weakest metal ligand in the series, reveals that this enzyme is able to accommodate a dinuclear center and that perturbations in the active site are limited to the Zn2 site. It is proposed that the role of Asp-120 is to act as a strong Zn2 ligand, locating this ion optimally for substrate binding, stabilization of the development of a partial negative charge in the β-lactam nitrogen, and protonation of this atom by a zinc-bound water molecule

Rotational spectrum of cis–cis HOONO

The pure rotational spectrum of cis-cis peroxynitrous acid, HOONO, has been observed. Over 220 transitions, sampling states up to J(')=67 and K-a(')=31, have been fitted with an rms uncertainty of 48.4 kHz. The experimentally determined rotational constants agree well with ab initio values for the cis-cis conformer, a five-membered ring formed by intramolecular hydrogen bonding. The small, positive inertial defect Delta=0.075667(60) amu A(2) and lack of any observable torsional splittings in the spectrum indicate that cis-cis HOONO exists in a well-defined planar structure at room temperature

Bs Mixing and Electric Dipole Moments in MFV

We analyze the general structure of four-fermion operators capable of introducing CP-violation preferentially in Bs mixing within the framework of Minimal Flavor Violation. The effect requires a minimum of O(Yu^4 Yd^4) Yukawa insertions, and at this order we find a total of six operators with different Lorentz, color, and flavor contractions that lead to enhanced Bs mixing. We then estimate the impact of these operators and of their close relatives on the possible sizes of electric dipole moments (EDMs) of neutrons and heavy atoms. We identify two broad classes of such operators: those that give EDMs in the limit of vanishing CKM angles, and those that require quark mixing for the existence of non-zero EDMs. The natural value for EDMs from the operators in the first category is up to an order of magnitude above the experimental upper bounds, while the second group predicts EDMs well below the current sensitivity level. Finally, we discuss plausible UV-completions for each type of operator.Comment: 11 pages; v2: references adde