On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients

We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U_q(su(3)). We obtain a very compact general analytical formula for the U_q(su(3)) CGCs in terms of the U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei), (2001

Mid-ocean ridge eruptions as a climate valve

Seafloor eruption rates and mantle melting fueling eruptions may be influenced by sea level and crustal loading cycles at scales from fortnightly to 100 kyr. Recent mid-ocean ridge eruptions occur primarily during neap tides and the first 6 months of the year, suggesting sensitivity to minor changes in tidal forcing and orbital eccentricity. An ~100 kyr periodicity in fast-spreading seafloor bathymetry and relatively low present-day eruption rates at a time of high sea level and decreasing orbital eccentricity suggest a longer-term sensitivity to sea level and orbital variations associated with Milankovitch cycles. Seafloor spreading is considered a small but steady contributor of CO2 to climate cycles on the 100 kyr time scale; however, this assumes a consistent short-term eruption rate. Pulsing of seafloor volcanic activity may feed back into climate cycles, possibly contributing to glacial/interglacial cycles, the abrupt end of ice ages, and dominance of the 100 kyr cycle

Resolved Stellar Populations at the Distance of Virgo

Top of the wish list of any astronomer who wants to understand galaxy formation and evolution is to resolve the stellar populations of a sample of giant elliptical galaxies: to take spectra of the stars and make Colour-Magnitude Diagrams going down to the oldest main sequence turn-offs. It is only by measuring the relative numbers of stars on Main Sequence Turnoffs at ages ranging back to the time of the earliest star formation in the Universe that we can obtain unambiguous star formation histories. Understanding star formation histories of individual galaxies underpins all our theories of galaxy formation and evolution. To date we only have detailed star formation histories for the nearest-by objects in the Local Group, namely galaxies within 700kpc of our own. This means predominantly small diffuse dwarf galaxies in a poor group environment. To sample the full range of galaxy types and to consider galaxies in a high density environment (where much mass in the Universe resides) we need to be able to resolve stars at the distance of the Virgo (~17Mpc) or Fornax (~18Mpc) clusters. This ambitious goal requires an Extremely Large Telescope (ELT), with a diameter of 50-150m, operating in the optical/near-IR at its diffraction limit.Comment: proceedings IAU 232 "Extremely Large Telescopes", eds Whitelock, Leibundgut and Dennefel

Unified description of quantum affine (super)algebras U_q(A_{1}^{(1)}) and U_q(C(2)^{(2)})

We show that the quantum affine algebra U_{q}(A_{1}^{(1)}) and the quantum affine superalgebra U_{q}(C(2)^{(2)}) admit unified description. The difference between them consists in the phase factor which is equal to 1 for U_{q}(A_{1}^{(1)}) and is equal to -1 for U_{q}(C(2)^{(2)}). We present such a description for the construction of Cartan-Weyl generators and their commutation relations, as well for the universal R-matrices.Comment: 16 pages, LaTeX. Talk by V.N. Tolstoy at XIV-th Max Born Symposium "New Symmetries and Integrable Models", Karpacz, September 1999; in press in Proceedings, Ed. World Scientific, 200

Extremal projectors for contragredient Lie (super)symmetries (short review)

A brief review of the extremal projectors for contragredient Lie (super)symmetries (finite-dimensional simple Lie algebras, basic classical Lie superalgebras, infinite-dimensional affine Kac-Moody algebras and superalgebras, as well as their quantum $q$-analogs) is given. Some bibliographic comments on the applications of extremal projectors are presented.Comment: 21 pages, LaTeX; typos corrected, references adde

Quantum Affine (Super)Algebras Uq(A1(1))U_q(A_{1}^{(1)}) and Uq(C(2)(2))U_q(C(2)^{(2)})

We show that the quantum affine algebra $U_{q}(A_{1}^{(1)})$ and the quantum affine superalgebra $U_{q}(C(2)^{(2)})$ admit a unified description. The difference between them consists in the phase factor which is equal to 1 for $U_{q}(A_{1}^{(1)})$ and it is equal to -1 for $U_{q}(C(2)^{(2)})$. We present such a description for the actions of the braid group, for the construction of Cartan-Weyl generators and their commutation relations, as well for the extremal projector and the universal R-matrix. We give also a unified description for the 'new realizations' of these algebras together with explicit calculations of corresponding R-matrices.Comment: 22 pages, LaTe

Neutral hydrogen in the starburst galaxy NGC3690/IC694

Researchers made observations of the neutral hydrogen (HI) emission structure surrounding the very deep absorption peak (observed earlier by Dickey (1986)) in the galaxy pair NGC3690/IC694. This galaxy pair is highly luminous in the far infrared, and known to exhibit extensive star formation as well as nuclear activity. Knowledge of the spatial distribution and velocity structure of the HI emission is of great importance to the understanding of the dynamics of the interaction and the resulting environmental effects on the galaxies

q-Analog of Gelfand-Graev Basis for the Noncompact Quantum Algebra U_q(u(n,1))

For the quantum algebra U_q(gl(n+1)) in its reduction on the subalgebra U_q(gl(n)) an explicit description of a Mickelsson-Zhelobenko reduction Z-algebra Z_q(gl(n+1),gl(n)) is given in terms of the generators and their defining relations. Using this Z-algebra we describe Hermitian irreducible representations of a discrete series for the noncompact quantum algebra U_q(u(n,1)) which is a real form of U_q(gl(n+1)), namely, an orthonormal Gelfand-Graev basis is constructed in an explicit form.Comment: Invited talk given by V.N.T. at XVIII International Colloquium "Integrable Systems and Quantum Symmetries", June 18--20, 2009, Prague, Czech Republi