A note on the tensor product of restricted simple modules for algebraic groups

Let G be a semisimple simply connected algebraic group over an algebraically closed field of positive characteristic p. Denote by G1 its first Frobenius kernel. In this note, we determine for which group G the restriction to G1 of any indecomposable G-summand of the tensor product of any two restricted simple G-modules remains indecomposable

Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels

Let G be a semisimple connected simply connected linear algebraic group over an algebraically closed field k of characteristic p > 0. Denote by Gn its nth Frobenius kernel and by G(pn) its finite subgroup of Fpn-rational points. In this paper we find quotients of the algebra Un = k[Gn]* and of the group algebra kG(pn) whose module category is equivalent to a (highest weight) subcategory of the category of rational G-modules

The blocks of the Brauer algebra in characteristic zero

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra

The measurement of the film thickness and the roughness deformation of lubricated elastomers

xiii+249hlm.;24c

Estimating Effects and Making Predictions from Genome-Wide Marker Data

In genome-wide association studies (GWAS), hundreds of thousands of genetic markers (SNPs) are tested for association with a trait or phenotype. Reported effects tend to be larger in magnitude than the true effects of these markers, the so-called ``winner's curse.'' We argue that the classical definition of unbiasedness is not useful in this context and propose to use a different definition of unbiasedness that is a property of the estimator we advocate. We suggest an integrated approach to the estimation of the SNP effects and to the prediction of trait values, treating SNP effects as random instead of fixed effects. Statistical methods traditionally used in the prediction of trait values in the genetics of livestock, which predates the availability of SNP data, can be applied to analysis of GWAS, giving better estimates of the SNP effects and predictions of phenotypic and genetic values in individuals.Comment: Published in at http://dx.doi.org/10.1214/09-STS306 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org