The space of unipotently supported class functions on a finite reductive group

We determine the Lusztig restrictions on the space of class functions with a unipotent support on a finite reductive group. In particular we give a simple expression for the Lusztig restrictions of the generalized Green functions and we describe the Lusztig restrictions of the generalized Gelfand-Graev representations. We make explicit computations for the Gelfand-Graev representations associated to the subregular unipotent class. In the case of SLn we show that the computations can be reduced to the case of GLn' for various n'.Comment: 21 page

The Impact of Poor Health on Education: New Evidence Using Genetic Markers

This paper examines the influence of health conditions on academic performance during adolescence. To account for the endogeneity of health outcomes and their interactions with risky behaviors we exploit natural variation within a set of genetic markers across individuals. We present strong evidence that these genetic markers serve as valid instruments with good statistical properties for ADHD, depression and obesity. They help to reveal a new dynamism from poor health to lower academic achievement with substantial heterogeneity in their impacts across genders. Our investigation further exposes the considerable challenges in identifying health impacts due to the prevalence of comorbid health conditions and endogenous health behaviors.health, education, genetic predisposition, obesity, ADHD, depression, instrumental variables, risky health behaviors

The Impact of Poor Health on Education: New Evidence Using Genetic Markers

This paper examines the influence of health conditions on academic performance during adolescence. To account for the endogeneity of health outcomes and their interactions with risky behaviors we exploit natural variation within a set of genetic markers across individuals. We present strong evidence that these genetic markers serve as valid instruments with good statistical properties for ADHD, depression and obesity. They help to reveal a new dynamism from poor health to lower academic achievement with substantial heterogeneity in their impacts across genders. Our investigation further exposes the considerable challenges in identifying health impacts due to the prevalence of comorbid health conditions and endogenous health behaviors.

Orientational order on curved surfaces - the high temperature region

We study orientational order, subject to thermal fluctuations, on a fixed curved surface. We derive, in particular, the average density of zeros of Gaussian distributed vector fields on a closed Riemannian manifold. Results are compared with the density of disclination charges obtained from a Coulomb gas model. Our model describes the disordered state of two dimensional objects with orientational degrees of freedom, such as vector ordering in Langmuir monolayers and lipid bilayers above the hexatic to fluid transition.Comment: final version, 13 Pages, 2 figures, uses iopart.cl

Computations for Coxeter arrangements and Solomon's descent algebra II: Groups of rank five and six

In recent papers we have refined a conjecture of Lehrer and Solomon expressing the character of a finite Coxeter group $W$ acting on the $p$th graded component of its Orlik-Solomon algebra as a sum of characters induced from linear characters of centralizers of elements of $W$. Our refined conjecture relates the character above to a component of a decomposition of the regular character of $W$ related to Solomon's descent algebra of $W$. The refined conjecture has been proved for symmetric and dihedral groups, as well as finite Coxeter groups of rank three and four. In this paper, the second in a series of three dealing with groups of rank up to eight (and in particular, all exceptional Coxeter groups), we prove the conjecture for finite Coxeter groups of rank five and six, further developing the algorithmic tools described in the previous article. The techniques developed and implemented in this paper provide previously unknown decompositions of the regular and Orlik-Solomon characters of the groups considered.Comment: Final Version. 17 page