R-matrices and Tensor Product Graph Method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.Comment: LaTex 7 pages. Contribution to the APCTP-Nankai Joint Symposium on "Lattice Statistics and Mathematical Physics", 8-10 October 2001, Tianjin, Chin

Quantum Lie algebras; their existence, uniqueness and qq-antisymmetry

Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized enveloping algebras. On them the quantum Lie bracket is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra g an abstract quantum Lie algebra g_h independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras are isomorphic to an abstract quantum Lie algebra g_h. In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras associated to the same g are isomorphic, 2) the quantum Lie bracket of any quantum Lie algebra is $q$-antisymmetric. We also describe a construction of quantum Lie algebras which establishes their existence.Comment: 18 pages, amslatex. Files also available from http://www.mth.kcl.ac.uk/~delius/q-lie/qlie_biblio/qlieuniq.htm

WFIRST Ultra-Precise Astrometry II: Asteroseismology

WFIRST microlensing observations will return high-precision parallaxes, sigma(pi) < 0.3 microarcsec, for the roughly 1 million stars with H<14 in its 2.8 deg^2 field toward the Galactic bulge. Combined with its 40,000 epochs of high precision photometry (~0.7 mmag at H_vega=14 and ~0.1 mmag at H=8), this will yield a wealth of asteroseismic data of giant stars, primarily in the Galactic bulge but including a substantial fraction of disk stars at all Galactocentric radii interior to the Sun. For brighter stars, the astrometric data will yield an external check on the radii derived from the two asteroseismic parameters, and nu_max, while for the fainter ones, it will enable a mass measurement from the single measurable asteroseismic parameter nu_max. Simulations based on Kepler data indicate that WFIRST will be capable of detecting oscillations in stars from slightly less luminous than the red clump to the tip of the red giant branch, yielding roughly 1 million detections.Comment: 13 pages, 6 figures, submitted to JKA

Quantum affine algebras and universal R-matrix with spectral parameter, II

This paper is an extended version of our previous short letter \cite{ZG2} and is attempted to give a detailed account for the results presented in that paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra and $U_q({\cal G})$ be the corresponding quantum simple Lie algebra. Using the previous obtained universal $R$-matrix for $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal $R$-matrix for $U_q(A_1)$ and $U_q(A_2)$. We apply these spectral-dependent universal $R$-matrix to some concrete representations. We then reproduce the well-known results for the fundamental representations and we are also able to derive for the first time the extreamly explicit and compact formula of the spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the simplest nontrival case when the tensor product of the representations is {\em not} multiplicity-free.Comment: 22 page

Quasi-Hopf Superalgebras and Elliptic Quantum Supergroups

We introduce the quasi-Hopf superalgebras which are $Z_2$ graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is the face type $B_{q,\lambda}(G)$ and the vertex type $A_{q,p}[\hat{sl(n|n)}]$ (and $A_{q,p}[\hat{gl(n|n)}]$), where $G$ is any Kac-Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for $U_q[\hat{sl(n|n)}]$ in a non-standard system of simple roots, all of which are fermionic.Comment: 22 pages, Latex fil

Turbulence characteristics of an axisymmetric reacting flow

Turbulent sudden expansion flows are of significant theoretical and practical importance. Such flows have been the subject of extensive analytical and experimental study for decades, but many issues are still unresolved. Detailed information on reacting sudden expansion flows is very limited, since suitable measurement techniques have only been available in recent years. The present study of reacting flow in an axisymmetric sudden expansion was initiated under NASA support in December 1983. It is an extension of a reacting flow program which has been carried out with Air Force support under Contract F33615-81-K-2003. Since the present effort has just begun, results are not yet available. Therefore a brief overview of results from the Air Force program will be presented to indicate the basis for the work to be carried out

Does Quality Time Produce Quality Children? Evidence on the Intergenerational Transmission of Human Capital Using Parental Deaths

This paper uses variation created by parental deaths in the amount of time children spend with each parent to examine whether the parent-child correlation in schooling outcomes stems from a causal relationship. Using a large sample of Israeli children who lost one parent during childhood, we find a series of striking patterns which show that the relationship is largely causal. Relative to children who did not lose a parent, the education of the deceased parent is less important in determining child outcomes, while the education of the surviving parent becomes a stronger factor. Moreover, within the group of families that lost a parent, this pattern intensifies when a child loses a parent earlier in life – the education of the deceased parent becomes even less important, while the effect of the surviving parent's schooling intensifies. These results provide strong evidence that there is a causal connection between parent and child schooling, which is dependent on the child's interaction time with each parent. These findings help us understand why educated parents typically spend more time with their children – they are more effective in producing human capital in their children.intergenerational mobility, education

Terror and the Costs of Crime

This paper argues that terrorism, beyond its immediate impact on innocent victims, also raises the costs of crime, and therefore, imposes a negative externality on potential criminals. Terrorism raises the costs of crime through two channels: (i) by increasing the presence and activity of the police force, and (ii) causing more people to stay at home rather than going out for leisure activities. Our analysis exploits a panel of 120 fatal terror attacks and all reported crimes for 17 districts throughout Israel between 2000 and 2005. After controlling for the fixed-effect of each district and for district-specific time trends, we show that terror attacks reduce property crimes such as burglary, auto-theft, and thefts-from-cars. Terror also reduces assaults and aggravated assaults which occur in private homes, but increases incidents of trespassing and "disrupting the police." Taken as a whole, the results are consistent with a stronger deterrence effect produced by an increased police presence after a terror attack. A higher level of policing is likely to catch more people trespassing, and at the same time, reduce the number of property crimes. The decline in crimes committed in private houses is likely an indication that the tendency for individuals to stay home after a terror attack further increases the costs of crime.crime, police, terror