Measurement of the Intensity of Turbulence

Spectral broadening of scattered light using Doppler heterodyne technique, and velocity profiles for laminar flow in a duc

Separate reference beam holographic interferometry and its application to the measurement of small phase variations in sub-fringe systems

Application of separate reference beam holographic interferometry for measurement of small phase variations in sub-fringe system

Completely reducible SL(2)-homomorphisms

Let K be any field, and let G be a semisimple group over K. Suppose the characteristic of K is positive and is very good for G. We describe all group scheme homomorphisms phi:SL(2) --> G whose image is geometrically G-completely reducible -- or G-cr -- in the sense of Serre; the description resembles that of irreducible modules given by Steinberg's tensor product theorem. In case K is algebraically closed and G is simple, the result proved here was previously obtained by Liebeck and Seitz using different methods. A recent result shows the Lie algebra of the image of phi to be geometrically G-cr; this plays an important role in our proof.Comment: AMS LaTeX 20 page

On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups

Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose also that $G$ is a classical group with natural module $W$, chosen minimally with respect to containing the image of $H$ under the associated representation. We consider the question of when $H$ can act irreducibly on a $G$-constituent of $W^{\otimes e}$ and study its relationship to the maximal subgroup problem for finite classical groups.Comment: To appear in Journal of Pure and Applied Algebr

Classical calculations of differential scattering cross sections for various screened potentials

Call number: LD2668 .T4 1969 T47Master of Scienc

Irreducible subgroups of simple algebraic groups - a survey

Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial finite dimensional irreducible rational $KG$-module. We say that $(G,H,V)$ is an irreducible triple if $V$ is irreducible as a $KH$-module. Determining these triples is a fundamental problem in the representation theory of algebraic groups, which arises naturally in the study of the subgroup structure of classical groups. In the 1980s, Seitz and Testerman extended earlier work of Dynkin on connected subgroups in characteristic zero to all algebraically closed fields. In this article we will survey recent advances towards a classification of irreducible triples for all positive dimensional subgroups of simple algebraic groups.Comment: 31 pages; to appear in the Proceedings of Groups St Andrews 201