82,381 research outputs found
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
Representations of Truncated Current Lie Algebras
Let g denote a Lie algebra, 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. The highest-weight representation theory of T(g) is
developed, and a reducibility criterion for the Verma modules is described.Comment: 5 pages. A summary of the article 'Highest-Weight Theory for
Truncated Current Lie Algebras' published on the arxi
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
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