Schur Partial Derivative Operators

A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice cells. The corresponding lattice diagram determinant is \Delta_L(X;Y)=\det \| x_i^{p_j}y_i^{q_j} \|. These lattice diagram determinants are crucial in the study of the so-called ``n! conjecture'' of A. Garsia and M. Haiman. The space M_L is the space spanned by all partial derivatives of \Delta_L(X;Y). The ``shift operators'', which are particular partial symmetric derivative operators are very useful in the comprehension of the structure of the M_L spaces. We describe here how a Schur function partial derivative operator acts on lattice diagrams with distinct cells in the positive quadrant.Comment: 8 pages, LaTe

Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n

The aim of this work is to study the quotient ring R_n of the ring Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous quasi-symmetric functions. We prove here that the dimension of R_n is given by C_n, the n-th Catalan number. This is also the dimension of the space SH_n of super-covariant polynomials, that is defined as the orthogonal complement of J_n with respect to a given scalar product. We construct a basis for R_n whose elements are naturally indexed by Dyck paths. This allows us to understand the Hilbert series of SH_n in terms of number of Dyck paths with a given number of factors.Comment: LaTeX, 3 figures, 12 page

Cool White Dwarfs Identified in the Second Data Release of the UKIRT Infrared Deep Sky Survey

We have paired the Second Data Release of the Large Area Survey of the UKIRT Infrared Deep Sky Survey with the Fifth Data Release of the Sloan Digital Sky Survey to identify ten cool white dwarf candidates, from their photometry and astrometry. Of these ten, one was previously known to be a very cool white dwarf. We have obtained optical spectroscopy for seven of the candidates using the GMOS-N spectrograph on Gemini North, and have confirmed all seven as white dwarfs. Our photometry and astrometry indicates that the remaining two objects are also white dwarfs. Model analysis of the photometry and available spectroscopy shows that the seven confirmed new white dwarfs, and the two new likely white dwarfs, have effective temperatures in the range Teff = 5400-6600 K. Our analysis of the previously known white dwarf confirms that it is cool, with Teff = 3800 K. The cooling age for this dwarf is 8.7 Gyr, while that of the nine ~6000 K white dwarfs is 1.8-3.6 Gyr. We are unable to determine the masses of the white dwarfs from the existing data, and therefore we cannot constrain the total ages of the white dwarfs. The large cooling age for the coolest white dwarf in the sample, combined with its low estimated tangential velocity, suggests that it is an old member of the thin disk, or a member of the thick disk of the Galaxy, with an age 10-11 Gyr. The warmer white dwarfs appear to have velocities typical of the thick disk or even halo; these may be very old remnants of low-mass stars, or they may be relatively young thin disk objects with unusually high space motion.Comment: 37 pages (referee format), 4 tables, 7 figures, accepted to Ap

Optical properties and spatial distribution of MgII absorbers from SDSS image stacking

We present a statistical analysis of the photometric properties and spatial distribution of more than 2,800 MgII absorbers with 0.37<z<1 and rest equivalent width W_0(\lambda2796)>0.8\AA detected in SDSS quasar spectra. Using an improved image stacking technique, we measure the cross-correlation between MgII gas and light (in the g, r, i and z-bands) from 10 to 200 kpc and infer the light-weighted impact parameter distribution of MgII absorbers. Such a quantity is well described by a power-law with an index that strongly depends on W_0, ranging from ~-1 for W_0~ 1.5\AA. At redshift 0.37<z<0.55, we find the average luminosity enclosed within 100 kpc around MgII absorbers to be M_g=-20.65+-0.11 mag, which is ~0.5 L_g*. The global luminosity-weighted colors are typical of present-day intermediate type galaxies. However, while the light of weaker absorbers originates mostly from red passive galaxies, stronger systems display the colors of blue star-forming galaxies. Based on these observations, we argue that the origin of strong MgII absorber systems might be better explained by models of metal-enriched gas outflows from star-forming/bursting galaxies. Our analysis does not show any redshift dependence for both impact parameter and rest-frame colors up to z=1. However, we do observe a brightening of the absorbers related light at high redshift (~50% from z~0.4 to 1). We argue that MgII absorbers are a phenomenon typical of a given evolutionary phase that more massive galaxies experience earlier than less massive ones, in a downsizing fashion. (abridged)Comment: ApJ in press, 28 pages, 16 figures, using emulateapj. Only typo corrections wrt the original submission (v1

On the Connection Between Metal Absorbers and Quasar Nebulae

We establish a simple model for the distribution of cold gas around L* galaxies using a large set of observational constraints on the properties of strong MgII absorber systems. Our analysis suggests that the halos of L* galaxies are filled with cool gaseous clouds having sizes of order 1kpc and densities of ~10^{-2} cm^{-3}. We then investigate the physical effects of cloud irradiation by a quasar and study the resulting spectral signatures. We show that quasar activity gives rise to (i) extended narrow-line emission on ~100kpc scales and (ii) an anisotropy in the properties of the absorbing gas arising from the geometry of the quasar radiation field. Provided that quasars reside in halos several times more massive than those of L* galaxies, our model predictions appear to be in agreement with observations of narrow emission-line nebulae around quasars and the recent detections of ~100kpc cold gaseous envelopes around those objects, suggesting a common origin for these phenomena. We discuss the implications of our results for understanding absorption systems, probing quasar environments at high redshifts, and testing the quasar unification scheme.Comment: 15 pages, 13 figures (ApJ submitted