10,395 research outputs found
Quantum Lie algebras; their existence, uniqueness and -antisymmetry
Quantum Lie algebras are generalizations of Lie algebras which have the
quantum parameter h built into their structure. They have been defined
concretely as certain submodules of the quantized enveloping algebras. On them
the quantum Lie bracket is given by the quantum adjoint action.
Here we define for any finite-dimensional simple complex Lie algebra g an
abstract quantum Lie algebra g_h independent of any concrete realization. Its
h-dependent structure constants are given in terms of inverse quantum
Clebsch-Gordan coefficients. We then show that all concrete quantum Lie
algebras are isomorphic to an abstract quantum Lie algebra g_h.
In this way we prove two important properties of quantum Lie algebras: 1) all
quantum Lie algebras associated to the same g are isomorphic, 2) the quantum
Lie bracket of any quantum Lie algebra is -antisymmetric. We also describe a
construction of quantum Lie algebras which establishes their existence.Comment: 18 pages, amslatex. Files also available from
http://www.mth.kcl.ac.uk/~delius/q-lie/qlie_biblio/qlieuniq.htm
Turbulence characteristics of an axisymmetric reacting flow
Turbulent sudden expansion flows are of significant theoretical and practical importance. Such flows have been the subject of extensive analytical and experimental study for decades, but many issues are still unresolved. Detailed information on reacting sudden expansion flows is very limited, since suitable measurement techniques have only been available in recent years. The present study of reacting flow in an axisymmetric sudden expansion was initiated under NASA support in December 1983. It is an extension of a reacting flow program which has been carried out with Air Force support under Contract F33615-81-K-2003. Since the present effort has just begun, results are not yet available. Therefore a brief overview of results from the Air Force program will be presented to indicate the basis for the work to be carried out
Photometric Selection of QSO Candidates From GALEX Sources
We present a catalog of 36,120 QSO candidates from the Galaxy Evolution
Explorer (GALEX) Release Two (GR2) UV catalog and the USNO-A2.0 optical
catalog. The selection criteria are established using known quasars from the
Sloan Digital Sky Survey (SDSS). The SDSS sample is then used to assign
individual probabilities to our GALEX-USNO candidates. The mean probability is
~50%, and would rise to ~65% if better morphological information than that from
USNO were available to eliminate galaxies. The sample is ~40% complete for
i<=19.1. Candidates are cross-identified in 2MASS, FIRST, SDSS, and XMM-Newton
Slewing Survey (XMMSL1), whenever such counterparts exist. The present catalog
covers the 8000 square degrees of GR2 lying above 25 degrees Galactic latitude,
but can be extended to all 24,000 square degress that satisfy this criterion as
new GALEX data become available.Comment: AASTeX v5.2, 31 pages, 9 figures. Accepted for publication in ApJ.
Extended tables available in the online edition of the journa
Interaction of a Modulated Electron Beam with a Plasma
The results of a theoretical and experimental investigation of the high-frequency interaction of an electron beam with a plasma are reported. An electron beam, modulated at a microwave frequency, passes through a uniform region of a mercury arc discharge after which it is demodulated. Exponentially growing wave amplification along the electron beam was experimentally observed for the first time at a microwave frequency equal to the plasma frequency. Approximate theories of the effects of 1) plasma-electron collision frequencies, 2) plasma-electron thermal velocities and 3) finite beam diameter, are given. In a second experiment the interaction between a modulated electron beam and a slow electrostatic wave on a plasma column has been studied. A strong interaction occurs when the velocity of the electron beam is approximately equal to the velocity of the wave and the interaction is essentially the same as that which occurs in traveling-wave amplifiers, except that here the plasma colum replaces the usual helical slow-wave circuit. The theory predicting rates of growth is presented and compared with the experimental results
Twisted quantum affine algebras and solutions to the Yang-Baxter equation
We construct spectral parameter dependent R-matrices for the quantized
enveloping algebras of twisted affine Lie algebras. These give new solutions to
the spectral parameter dependent quantum Yang-Baxter equation.Comment: Latex 24 pages. Misprints in eqs.(4.26) and (A.11) are corrected,
cosmetic changes from "affine Kac-Moody algebras" to "affine Lie algebras"
are made throughout the paper following a suggestion by M.B. Halpern, and one
reference is adde
Degenerate mixing of plasma waves on cold, magnetized single-species plasmas
In the cold-fluid dispersion relation ω = ω_p/[1+(k_⊥/k_z)^(2]1/2) for Trivelpiece-Gould waves on an infinitely long magnetized plasma cylinder, the transverse and axial wavenumbers appear only in the combination k_⊥/k_z. As a result, for any frequency ω<ω_p, there are infinitely many degenerate waves, all having the same value of k_⊥/k_z. On a cold finite-length plasma column, these degenerate waves reflect into one another at the ends; thus, each standing-wave normal mode of the bounded plasma is a mixture of many degenerate waves, not a single standing wave as is often assumed. A striking feature of the many-wave modes is that the short-wavelength waves often add constructively along resonance cones given by dz/dr = ±(ω_p^2/ω^2-1)^(1/2). Also, the presence of short wavelengths in the admixture for a predominantly long-wavelength mode enhances the viscous damping beyond what the single-wave approximation would predict. Here, numerical solutions are obtained for modes of a cylindrical plasma column with rounded ends. Exploiting the fact that the modes of a spheroidal plasma are known analytically (the Dubin modes), a perturbation analysis is used to investigate the mixing of low-order, nearly degenerate Dubin modes caused by small deformations of a plasma spheroid
Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: }
The type-I quantum superalgebras are known to admit non-trivial one-parameter
families of inequivalent finite dimensional irreps, even for generic . We
apply the recently developed technique to construct new solutions to the
quantum Yang-Baxter equation associated with the one-parameter family of irreps
of , thus obtaining R-matrices which depend not only on a
spectral parameter but in addition on further continuous parameters. These
extra parameters enter the Yang-Baxter equation in a similar way to the
spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected
On Type-I Quantum Affine Superalgebras
The type-I simple Lie-superalgebras are and . We study
the quantum deformations of their untwisted affine extensions
and . We identify additional
relations between the simple generators (``extra -Serre relations") which
need to be imposed to properly define \uqgh and . We
present a general technique for deriving the spectral parameter dependent
R-matrices from quantum affine superalgebras. We determine the R-matrices for
the type-I affine superalgebra in various representations,
thereby deriving new solutions of the spectral-dependent Yang-Baxter equation.
In particular, because this algebra possesses one-parameter families of
finite-dimensional irreps, we are able to construct R-matrices depending on two
additional spectral-like parameters, providing generalizations of the
free-fermion model.Comment: 23 page
Infinite Families of Gauge-Equivalent -Matrices and Gradations of Quantized Affine Algebras
Associated with the fundamental representation of a quantum algebra such as
or , there exist infinitely many gauge-equivalent
-matrices with different spectral-parameter dependences. It is shown how
these can be obtained by examining the infinitely many possible gradations of
the corresponding quantum affine algebras, such as and
, and explicit formulae are obtained for those two cases.
Spectral-dependent similarity (gauge) transformations relate the -matrices
in different gradations. Nevertheless, the choice of gradation can be
physically significant, as is illustrated in the case of quantum affine Toda
field theories.Comment: 14 pages, Latex, UQMATH-93-10 (final version for publication
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