Algebraic structure of multi-parameter quantum groups

Multi-parameter versions U_p(g) and C_p[G] of the standard quantum groups U_q(g) and C_q[G] are considered where G is a semi-simple connected complex algebraic group and g is the Lie algebra of G. The primitive spectrum of C_p[G] is calculated, generalizing a result of Joseph for the standard quantum groups. This classification is compared with the classification of symplectic leaves for the associated Poisson structure on G.Comment: AMS Latex, 37 pages, June 1994; to appear in Advances in Mat

Polarimetric observations of comet Levy 1990c and of other comets: Some clues to the evolution of cometary dust

The evolution with the phase angle alpha of the polarization degree P of light scattered by comet Halley's dust is well documented. No significant discrepancy is found between Halley and Levy polarization curves near the inversion point. From all available cometary observations, we have derived polarimetric synthetic curves. Typically, a set of about 200 data points in the red wavelengths range exhibits a minimum for (alpha approximately equals 10.3 degrees, P approximately equals 1.8 percent) and an inversion point for (alpha approximately equals 22.4 degrees, P = 0 percent), with a slop of about 0.27 percent per degree. A significant spreading of some data (comets Austin 1982VI, Austin 1989c1, West 1976VI) is found at large phase angles. The analysis of our polarimetric maps of Levy reveals that the inner coma is heterogeneous. The increase of the inversion angle value with increasing distance from the photometric center is suspected to be due to the evolution with time of grains ejected from the nucleus. A fan like structure could be produced by a jet of grains freshly ejected

Tidal currents, winds and the morphology of phytoplankton spatial structures

Chlorophyll a, nutrients and salinity distributions were studied at two spatial scales (10 cm and 0.25 to 2.5 km) in the St. Lawrence Estuary (Quebec, Canada), in order to investigate the role of tidal currents and winds in the formation and maintenance of spatial structures. Data were collected according to a synoptic sampling pattern using three sampling platforms simultaneously, and they were analyzed using analysis of variance. The sampling pattern was repeated on four occasions during July 1980.Analyses of variance indicated significant spatial heterogeneities of about the same magnitude at the two scales studied for chlorophyll and nutrients, whereas salinity showed only large–scale variability. At the kilometer scale, the frequency distribution spectra of patch length for chlorophyll showed the existence of patches of various dimensions between 0.2 and 6.0 km with a dominance of small patches (≤0.5 km). Frequency maxima were usually observed at the smaller (≤0.5 km) and larger (≥2.0 km) scales for the nutrients and only at larger (≥2.0 km) scale for salinity. The distribution spectra of patch dimensions were characteristic for each sampling experiment, depending on tidal currents and prevailing wind conditions. Estimated patch dimensions were larger parallel to the current direction than perpendicular to current direction, implying that spatial structures are elongated in the sense of the current direction. Higher winds have, first, a tendency to increase the small–scale structure of the environment by breaking up larger patches into smaller patches, before structures are completely eliminated. The implication of these findings is that different results could be obtained depending on the sampling strategy used (sampling either at anchor stations or at random, independent of current direction), which could lead to different conclusions

Benchmark calculations for elastic fermion-dimer scattering

We present continuum and lattice calculations for elastic scattering between a fermion and a bound dimer in the shallow binding limit. For the continuum calculation we use the Skorniakov-Ter-Martirosian (STM) integral equation to determine the scattering length and effective range parameter to high precision. For the lattice calculation we use the finite-volume method of L\"uscher. We take into account topological finite-volume corrections to the dimer binding energy which depend on the momentum of the dimer. After subtracting these effects, we find from the lattice calculation kappa a_fd = 1.174(9) and kappa r_fd = -0.029(13). These results agree well with the continuum values kappa a_fd = 1.17907(1) and kappa r_fd = -0.0383(3) obtained from the STM equation. We discuss applications to cold atomic Fermi gases, deuteron-neutron scattering in the spin-quartet channel, and lattice calculations of scattering for nuclei and hadronic molecules at finite volume.Comment: 16 pages, 5 figure

Quantum Hamiltonian Reduction for Polar Representations

Let $G$ be a reductive complex Lie group with Lie algebra $\mathfrak{g}$ and suppose that $V$ is a polar $G$-representation. We prove the existence of a radial parts map $\mathrm{rad}: \mathcal{D}(V)^G\to A_{\kappa}$ from the $G$-invariant differential operators on $V$ to the spherical subalgebra $A_{\kappa}$ of a rational Cherednik algebra. Under mild hypotheses $\mathrm{rad}$ is shown to be surjective. If $V$ is a symmetric space, then $\mathrm{rad}$ is always surjective, and we determine exactly when $A_{\kappa}$ is a simple ring. When $A_{\kappa}$ is simple, we also show that the kernel of $\mathrm{rad}$ is $\left(\mathcal{D}(V)\tau(\mathfrak{g}\right)^G$, where $\tau:\mathfrak{g}\to \mathcal{D}(V)$ is the differential of the $G$-action.Comment: 59 pages; minor typos and references update