Graded Contractions of Affine Kac-Moody Algebras

The method of graded contractions, based on the preservation of the automorphisms of finite order, is applied to the affine Kac-Moody algebras and their representations, to yield a new class of infinite dimensional Lie algebras and representations. After the introduction of the horizontal and vertical gradings, and the algorithm to find the horizontal toroidal gradings, I discuss some general properties of the graded contractions, and compare them with the In\"on\"u-Wigner contractions. The example of $\hat A_2$ is discussed in detail.Comment: 23 pages, Ams-Te

Clinic accessibility and clinic-level predictors of the geographic variation in 2009 pandemic influenza vaccine coverage in Montreal, Canada

Background: Nineteen mass vaccination clinics were established in Montreal, Canada, as part of the 2009 influenza A/H1N1p vaccination campaign. Although approximately 50% of the population was vaccinated, there was a considerable variation in clinic performance and community vaccine coverage. Objective: To identify community- and clinic-level predictors of vaccine uptake, while accounting for the accessibility of clinics from the community of residence. Methods: All records of influenza A/H1N1p vaccinations administered in Montreal were obtained from a vaccine registry. Multivariable regression models, specifically Bayesian gravity models, were used to assess the relationship between vaccination rates and clinic accessibility, clinic-level factors, and community-level factors. Results: Relative risks compare the vaccination rates at the variable's upper quartile to the lower quartile. All else being equal, clinics in areas with high violent crime rates, high residential density, and high levels of material deprivation tended to perform poorly (adjusted relative risk [ARR]: 0·917, 95% CI [credible interval]: 0·915, 0·918; ARR: 0·663, 95% CI: 0·660, 0·666, ARR: 0·649, 95% CI: 0·645, 0·654, respectively). Even after controlling for accessibility and clinic-level predictors, communities with a greater proportion of new immigrants and families living below the poverty level tended to have lower rates (ARR: 0·936, 95% CI: 0·913, 0·959; ARR: 0·918, 95% CI: 0·893, 0·946, respectively), while communities with a higher proportion speaking English or French tended to have higher rates (ARR: 1·034, 95% CI: 1·012, 1·059). Conclusion: In planning future mass vaccination campaigns, the gravity model could be used to compare expected vaccine uptake for different clinic location strategies

Production of Pairs of Sleptoquarks in Hadron Colliders

We calculate the cross section for the production of pairs of scalar leptoquarks (sleptoquarks) in a supersymmetric $E_6$ model, at hadron colliders. We estimate higher order corrections by including $\pi^2$ terms induced by soft-gluon corrections. Discovery bounds on the sleptoquark mass are estimated at collider energies of 1.8, 2, and 4 TeV (Tevatron), and 16 TeV (LHC).Comment: 8 pages, REVTEX, (1 fig. available on request), LAVAL-PHY-94-13/McGILL-94-26/SPhT-94-07

Casimir invariants for the complete family of quasi-simple orthogonal algebras

A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient "pyramidal" manner, in terms of certain sets of "Pauli-Lubanski" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given.Comment: 19 pages, LaTe

On the bicrossproduct structures for the Uλ(isoω2...ωN(N)){\cal U}_\lambda(iso_{\omega_2... \omega_N}(N)) family of algebras

It is shown that the family of deformed algebras ${\cal U}_\lambda(iso_{\omega_2... \omega_N}(N))$ has a different bicrossproduct structure for each $\omega_a=0$ in analogy to the undeformed case.Comment: Latex2e file. 14 page

Leptoquark pair production at the Fermilab Tevatron: Signal and backgrounds

We perform a Monte-Carlo simulation of scalar leptoquark pair production at the Tevatron (energy =1.8 TeV and luminosity =100 pb^{-1}) with ISAJET. We also investigate the dominant sources of Standard Model background: Z*jj, ZZ production and heavy quark top-antitop. We find that the top-antitop background is the most important except near the Z pole where the Z*jj background is peaked. We also evaluate the signal-to-background ratio and find a discovery reach of 130 GeV (170 GeV) for a branching ratio of B(LQ-> eq)=0.5 (B=1).Comment: 8 pages, 6 figures, latex (revtex

Boson representations, non-standard quantum algebras and contractions

A Gelfan'd--Dyson mapping is used to generate a one-boson realization for the non-standard quantum deformation of $sl(2,\R)$ which directly provides its infinite and finite dimensional irreducible representations. Tensor product decompositions are worked out for some examples. Relations between contraction methods and boson realizations are also explored in several contexts. So, a class of two-boson representations for the non-standard deformation of $sl(2,\R)$ is introduced and contracted to the non-standard quantum (1+1) Poincar\'e representations. Likewise, a quantum extended Hopf $sl(2,\R)$ algebra is constructed and the Jordanian $q$-oscillator algebra representations are obtained from it by means of another contraction procedure.Comment: 21 pages, LaTeX; two new references adde

Spin 1 fields in Riemann-Cartan space-times "via" Duffin-Kemmer-Petiau theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.Comment: 8 pages, no figures, revtex. Dedicated to Professor Gerhard Wilhelm Bund on the occasion of his 70th birthday. To appear in Gen. Rel. Grav. Equations numbering corrected. References update