A simplified proof of the reduction point crossing sign formula for Verma modules

The Unitary Dual Problem is one of the most important open problems in mathematics: classify the irreducible unitary representations of a group. That is, classify all irreducible representations admitting a definite invariant Hermitian form. Signatures of invariant Hermitian forms on Verma modules are important to finding the unitary dual of a real reductive Lie group. By a philosophy of Vogan introduced in [Vog84], signatures of invariant Hermitian forms on irreducible Verma modules may be computed by varying the highest weight and tracking how signatures change at reducibility points (see [Yee05]). At each reducibility point there is a sign ε governing how the signature changes. A formula for ε was first determined in [Yee05] and simplified in [Yee19]. The proof of the simplification was complicated. We simplify the proof in this note

Growth and properties of ferromagnetic In(1-x)Mn(x)Sb alloys

We discuss a new narrow-gap ferromagnetic (FM) semiconductor alloy, In(1-x)Mn(x)Sb, and its growth by low-temperature molecular-beam epitaxy. The magnetic properties were investigated by direct magnetization measurements, electrical transport, magnetic circular dichroism, and the magneto-optical Kerr effect. These data clearly indicate that In(1-x)Mn(x)Sb possesses all the attributes of a system with carrier-mediated FM interactions, including well-defined hysteresis loops, a cusp in the temperature dependence of the resistivity, strong negative magnetoresistance, and a large anomalous Hall effect. The Curie temperatures in samples investigated thus far range up to 8.5 K, which are consistent with a mean-field-theory simulation of the carrier-induced ferromagnetism based on the 8-band effective band-orbital method.Comment: Invited talk at 11th International Conference on Narrow Gap Semiconductors, Buffalo, New York, U.S.A., June 16 - 20, 200

External control of the direction of magnetization in ferromagnetic InMnAs/GaSb heterostructures

In this paper, we demonstrate external control over the magnetization direction in ferromagnetic (FM) In_{1-x}Mn_{x}As/GaSb heterostructures. FM ordering with T_C as high as 50 K is confirmed by SQUID magnetization, anomalous Hall effect (AHE), and magneto-optical Kerr effect (MOKE) measurements. Even though tensile strain is known to favor an easy axis normal to the layer plane, at low temperatures we observe that the magnetization direction in several samples is intermediate between the normal and in-plane axes. As the temperature increases, however, the easy axis rotates to the direction normal to the plane. We further demonstrate that the easy magnetization axis can be controlled by incident light through a bolometric effect, which induces a pronounced increase in the amplitude of the AHE. A mean-field-theory model for the carrier-mediated ferromagnetism reproduces the tendency for dramatic reorientations of the magnetization axis, but not the specific sensitivity to small temperature variations.Comment: 11 pages, 3 figures, submitted to NGS-1

Information (and library) science at City University London; 50 years of educational development

The development of education for information and library science at City University London over a 50-year period is described in this article. The development of the Masters course in Information Science, and the later equivalent courses in Library Science and in Information Management in the Cultural Sector are described in detail, together with shorter-lived Masters courses in pharmaceutical and health information. The rationale for changes to the courses, and the influence of the professional and educational contexts, are analysed. Issues emerging from this analysis are discussed in seven themes: the nature of the discipline; the library/information spectrum; the student group; the academic/professional balance; curriculum design; local and global issues; and teaching methods. The discussions of the courses are set in the wider context of changes in library/information education over the period in the UK and worldwide

Cosmological consequences of a Chaplygin gas dark energy

A combination of recent observational results has given rise to what is currently known as the dark energy problem. Although several possible candidates have been extensively discussed in the literature to date the nature of this dark energy component is not well understood at present. In this paper we investigate some cosmological implications of another dark energy candidate: an exotic fluid known as the Chaplygin gas, which is characterized by an equation of state $p = -A/\rho$, where $A$ is a positive constant. By assuming a flat scenario driven by non-relativistic matter plus a Chaplygin gas dark energy we study the influence of such a component on the statistical properties of gravitational lenses. A comparison between the predicted age of the universe and the latest age estimates of globular clusters is also included and the results briefly discussed. In general, we find that the behavior of this class of models may be interpreted as an intermediary case between the standard and $\Lambda$CDM scenarios.Comment: 7 pages, 5 figures, to appear in Phys. Rev.

The Singularity of Orbital Measures on Compact Lie Groups

We find the minimal real number k such that the kth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of Lp-improving measures