Highest-Weight Theory for Truncated Current Lie Algebras

Let g denote a Lie algebra over a field of characteristic zero, and let T(g) denote the tensor product of g with a ring of truncated polynomials. The Lie algebra T(g) is called a truncated current Lie algebra, or in the special case when g is finite-dimensional and semisimple, a generalized Takiff algebra. In this paper a highest-weight theory for T(g) is developed when the underlying Lie algebra g possesses a triangular decomposition. The principal result is the reducibility criterion for the Verma modules of T(g) for a wide class of Lie algebras g, including the symmetrizable Kac-Moody Lie algebras, the Heisenberg algebra, and the Virasoro algebra. This is achieved through a study of the Shapovalov form.Comment: 42 pages. An extract from the author's PhD thesis. See also: http://www.maths.usyd.edu.au/u/benw

An Education Carol

This work is rendition of a small play written by Ben Fruchtl. This work analyzes one of the essential questions of the course, Social Foundations of Music Education, and questions how educators can change models of education to make learning more relevant in and out of school

Gravitational waves from the r-modes of rapidly rotating neutron stars

Since the last Amaldi meeting in 1997 we have learned that the r-modes of rapidly rotating neutron stars are unstable to gravitational radiation reaction in astrophysically realistic conditions. Newborn neutron stars rotating more rapidly than about 100Hz may spin down to that frequency during up to one year after the supernova that gives them birth, emitting gravitational waves which might be detectable by the enhanced LIGO interferometers at a distance which includes several supernovae per year. A cosmological background of these events may be detectable by advanced LIGO. The spins (about 300Hz) of neutron stars in low-mass x-ray binaries may also be due to the r-mode instability (under different conditions), and some of these systems in our galaxy may also produce detectable gravitational waves--see the review by G. Ushomirsky in this volume. Much work is in progress on developing our understanding of r-mode astrophysics to refine the early, optimistic estimates of the detectability of the gravitational waves.Comment: 10 pages, 2 figures, 3rd Edoardo Amaldi Conference on Gravitational Wave

Sentenced for a “Crime” the Government Did Not Prove: Jones v. United States and the Constitutional Limitations on Factfinding by Sentencing Factors Rather Than Elements of the Offense

Priester argues that the Constitution does restrict the power of the legislature by requiring that certain facts be proved as elements of the offense. He notes the Supreme Court\u27s missed opportunity in Jones v. United States to adopt the test proposed by Justice Scalia