Modified Affine Hecke Algebras and Drinfeldians of Type A

We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l}) (\h{H}_{q\eta}({l})) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra \h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra \h{H}_{q}(l) of type $A_{l-1}$, if the parameter q goes to 1 the algebra \h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra \Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta}^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000

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

Q-power function over Q-commuting variables and deformed XXX, XXZ chains

We find certain functional identities for the Gauss q-power function of a sum of q-commuting variables. Then we use these identities to obtain two-parameter twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian Y(sl_2). We determine the corresponding deformed trigonometric and rational quantum R-matrices, which then are used in the computation of deformed XXX and XXZ Hamiltonians.Comment: LaTeX, 12 page

Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics

The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.Comment: 13 pages,LaTeX, v2. References added, typos correcte

Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems

A representation theory of the quantized Poincar\'e ($\kappa$-Poincar\'e) algebra (QPA) is developed. We show that the representations of this algebra are closely connected with the representations of the non-deformed Poincar\'e algebra. A theory of tensor operators for QPA is considered in detail. Necessary and sufficient conditions are found in order for scalars to be invariants. Covariant components of the four-momenta and the Pauli-Lubanski vector are explicitly constructed.These results are used for the construction of some q-relativistic equations. The Wigner-Eckart theorem for QPA is proven.Comment: 18 page

On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization

We study classical twists of Lie bialgebra structures on the polynomial current algebra $\mathfrak{g}[u]$, where $\mathfrak{g}$ is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric $r$-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of $\mathfrak{g}$. We give complete classification of quasi-trigonometric $r$-matrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root). We quantize solutions corresponding to the first root of $\mathfrak{sl}(n)$.Comment: 41 pages, LATE

Stellar Populations in the Phoenix Dwarf (dIrr/dSph) Galaxy as Observed by HST/WFPC2

We present HST/WFPC2 photometry of the central regions of the Phoenix dwarf. Accurate photometry allows us to: 1) confirm the existence of the horizontal branch previously detected by ground-based observations, and use it to determine a distance to Phoenix, 2) clearly detect the existence of multiple ages in the stellar population of Phoenix, 3) determine a mean metallicity of the old red giant branch stars in Phoenix, and suggest that Phoenix has evolved chemically over its lifetime, 4) extract a rough star formation history for the central regions which suggests that Phoenix has been forming stars roughly continuously over its entire lifetime.Comment: Accepted by AJ, 22 pages including 6 figures + 1 figure in JPEG forma

Study of the Sextans dwarf spheroidal galaxy from the DART Ca ii triplet survey

We use Very Large Telescope (VLT)/Fibre Large Array Multi Element Spectrograph (FLAMES) intermediate-resolution (R∼ 6500) spectra of individual red giant branch stars in the near-infrared Ca ii triplet (CaT) region to investigate the wide-area metallicity properties and internal kinematics of the Sextans dwarf spheroidal galaxy (dSph). Our final sample consists of 174 probable members of Sextans with accurate line-of-sight velocities (±2 km s−1) and CaT [Fe/H] measurements (±0.2 dex). We use the Mg i line at 8806.8 Å as an empirical discriminator for distinguishing between probable members of the dSph (giant stars) and probable Galactic contaminants (dwarf stars). Sextans shows a similar chemodynamical behaviour to other Milky Way dSphs, with its central regions being more metal rich than the outer parts and with the more metal-rich stars displaying colder kinematics than the more metal-poor stars. Hints of a velocity gradient are found along the projected major axis and along an axis at position angle (PA) = 191°, however, a larger and more spatially extended sample may be necessary to pin down the amplitude and direction of this gradient. We detect a cold kinematic substructure at the centre of Sextans, consistent with being the remnant of a disrupted very metal poor stellar cluster. We derive the most extended line-of-sight velocity dispersion profile for Sextans, out to a projected radius of 1°.6. From Jeans modelling of the observed line-of-sight velocity dispersion profile we find that this is consistent with both a cored dark matter halo with large core radius and cuspy halo with low concentration. The mass within the last measured point is in the range 2-4 × 108 M⊙, giving very large mass-to-light ratios, from 460 to 920 (M/L)V,

The early days of the Sculptor dwarf spheroidal galaxy

We present the high resolution spectroscopic study of five -3.9<=[Fe/H]<=-2.5 stars in the Local Group dwarf spheroidal, Sculptor, thereby doubling the number of stars with comparable observations in this metallicity range. We carry out a detailed analysis of the chemical abundances of alpha, iron peak, light and heavy elements, and draw comparisons with the Milky Way halo and the ultra faint dwarf stellar populations. We show that the bulk of the Sculptor metal-poor stars follows the same trends in abundance ratios versus metallicity as the Milky Way stars. This suggests similar early conditions of star formation and a high degree of homogeneity of the interstellar medium. We find an outlier to this main regime, which seems to miss the products of the most massive of the TypeII supernovae. In addition to its value to help refining galaxy formation models, this star provides clues to the production of cobalt and zinc. Two of our sample stars have low odd-to-even barium isotope abundance ratios, suggestive of a fair proportion of s-process; we discuss the implication for the nucleosynthetic origin of the neutron capture elements.Comment: Replacement after language editio

Deformation of orthosymplectic Lie superalgebra osp(1|2)

Triangular deformation of the orthosymplectic Lie superalgebra osp(1|4) is defined by chains of twists. Corresponding classical r-matrix is obtained by a contraction procedure from the trigonometric r-matrix. The carrier space of the constant r-matrix is the Borel subalgebra.Comment: LaTeX, 8 page