Algebras of invariant differential operators on a class of multiplicity free spaces

Let G be a connected reductive algebraic group and let G'=[G,G] be its derived subgroup. Let (G,V) be a multiplicity free representation with a one dimensional quotient (see definition below). We prove that the algebra D(V)^{G'} of G'-invariant differential operators with polynomial coefficients on V, is a quotient of a so-called Smith algebra over its center. Over C this class of algebras was introduced by S.P. Smith as a class of algebras similar to the enveloping algebra U(sl(2)) of sl(2). Our result generalizes the case of the Weil representation, where the associative algebra generated by Q(x) and Q(?) (Q being a non degenerate quadratic form on V) is a quotient of U(sl(2)) Other structure results are obtained when (G,V) is a regular prehomogeneous vector space of commutative parabolic type

Employment-Based Health Insurance: 2010

[Excerpt] This report uses data from the Survey of Income and Program Participation (SIPP) to examine the characteristics of people with employer-provided health insurance coverage as well as characteristics of employers that offer health insurance. This documentation of the current distribution of employment-based health insurance coverage across socioeconomic characteristics is needed to establish the changes associated with recent health care legislation. The report is composed of two sections. The first section provides a brief overview of historical trends in employer-provided coverage rates by source of coverage as well as the reasons for nonparticipation in health insurance from 1997 to 2010. The second section focuses on data collected in 2010 and describes health insurance offer and take-up rates by employee and employer characteristics. In addition, the report describes the insurance status of workers not participating in an employer’s plan and the reasons for nonparticipation

The Performance of Knowledge: Pointing and Knowledge in Powerpoint Presentations

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Powerpoint and similar technologies have contributed to a profound transformation of lecturing and presenting information. In focusing on pointing in powerpoint presentations, the article addresses aspects of this transformation of speech into 'presentations'. As opposed to popular attacks against powerpoint, the analysis of a large number of audio-visually recorded presentations (mainly in German) demonstrates the creativity of these 'performances', based on the interplay of slides (and other aspects of this technology), speech, pointing and body formations. Pointing seems to be a particular feature of this kind of presentation, allowing knowledge to be located in space. Considering powerpoint as one of the typical technologies of so-called 'knowledge societies', this aspect provides some indication as to the social understanding of knowledge. Instead of 'representing' reality, knowledge is defined by the circularity of speaking and showing, thus becoming presented knowledge rather than representing knowledge

Existence of an intermediate phase for oriented percolation

We consider the following oriented percolation model of $\mathbb {N} \times \mathbb{Z}^d$: we equip $\mathbb {N}\times \mathbb{Z}^d$ with the edge set $\{[(n,x),(n+1,y)] | n\in \mathbb {N}, x,y\in \mathbb{Z}^d\}$, and we say that each edge is open with probability $p f(y-x)$ where $f(y-x)$ is a fixed non-negative compactly supported function on $\mathbb{Z}^d$ with $\sum_{z\in \mathbb{Z}^d} f(z)=1$ and $p\in [0,\inf f^{-1}]$ is the percolation parameter. Let $p_c$ denote the percolation threshold ans $Z_N$ the number of open oriented-paths of length $N$ starting from the origin, and study the growth of $Z_N$ when percolation occurs. We prove that for if $d\ge 5$ and the function $f$ is sufficiently spread-out, then there exists a second threshold $p_c^{(2)}>p_c$ such that $Z_N/p^N$ decays exponentially fast for $p\in(p_c,p_c^{(2)})$ and does not so when $p> p_c^{(2)}$. The result should extend to the nearest neighbor-model for high-dimension, and for the spread-out model when $d=3,4$. It is known that this phenomenon does not occur in dimension 1 and 2.Comment: 16 pages, 2 figures, further typos corrected, enlarged intro and bibliograph