767 research outputs found
The quantum Casimir operators of \Uq and their eigenvalues
We show that the quantum Casimir operators of the quantum linear group
constructed in early work of Bracken, Gould and Zhang together with one extra
central element generate the entire center of \Uq. As a by product of the
proof, we obtain intriguing new formulae for eigenvalues of these quantum
Casimir operators, which are expressed in terms of the characters of a class of
finite dimensional irreducible representations of the classical general linear
algebra.Comment: 10 page
A symmetry invariant integral on kappa-deformed spacetime
In this note we present an approach using both constructive and Hopf
algebraic methods to contribute to the not yet fully satisfactory definition of
an integral on kappa-deformed spacetime. The integral presented here is based
on the inner product of differential forms and it is shown that this integral
is explicitly invariant under the deformed symmetry structure.Comment: 16 page
Chaotic Accretion in a Non-Stationary Electromagnetic Field of a Slowly Rotating Compact Star
We investigate charge accretion in vicinity of a slowly rotating compact star
with a non-stationary electromagnetic field. Exact solutions to the general
relativistic Maxwell equations are obtained for a star formed of a highly
degenerate plasma with a gravitational field given by the linearized Kerr
metric. These solutions are used to formulate and then to study numerically the
equations of motion for a charged particle in star's vicinity using the
gravitoelectromagnetic force law. The analysis shows that close to the star
charge accretion does not always remain ordered. It is found that the magnetic
field plays the dominant role in the onset of chaos near the star's surface.Comment: 9 pages, 4 figure
Restricted infinitesimal deformations of restricted simple Lie algebras
We compute the restricted infinitesimal deformations of the restricted simple
Lie algebras over an algebraically closed field of characteristic different
from 2 and 3.Comment: 15 pages; final version, to appear in Journal of Algebra and Its
Application
Notes on two-parameter quantum groups, (I)
A simpler definition for a class of two-parameter quantum groups associated
to semisimple Lie algebras is given in terms of Euler form. Their positive
parts turn out to be 2-cocycle deformations of each other under some
conditions. An operator realization of the positive part is given.Comment: 11 page
On dual canonical bases
The dual basis of the canonical basis of the modified quantized enveloping
algebra is studied, in particular for type . The construction of a basis for
the coordinate algebra of the quantum matrices is appropriate for
the study the multiplicative property. It is shown that this basis is invariant
under multiplication by certain quantum minors including the quantum
determinant. Then a basis of quantum SL(n) is obtained by setting the quantum
determinant to one. This basis turns out to be equivalent to the dual canonical
basis
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Quasicrystalline Approach to Predicting the Spinel-Nepheline Liquidus: Application to Nuclear Waste Glass Processing
The crystal-melt equilibria in complex fifteen component melts are modeled based on quasicrystalline concepts. A pseudobinary phase diagram between acmite (which melts incongruently to a transition metal ferrite spinel) and nepheline is defined. The pseudobinary lies within the Al{sub 2}O{sub 3}-Fe{sub 2}O{sub 3}-Na{sub 2}O-SiO{sub 2} quaternary system that defines the crystallization of basalt glass melts. The pseudobinary provides the partitioning of species between the melt and the primary liquidus phases. The medium range order of the melt and the melt-crystal exchange equilibria are defined based on a constrained mathematical treatment that considers the crystallochemical coordination of the elemental species in acmite and nepheline. The liquidus phases that form are shown to be governed by the melt polymerization and the octahedral site preference energies. This quasicrystalline liquidus model has been used to prevent unwanted crystallization in the world's largest high level waste (HLW) melter for the past three years while allowing >10 wt% higher waste loadings to be processed
Electroweak Sudakov Logarithms and Real Gauge-Boson Radiation in the TeV Region
Electroweak radiative corrections give rise to large negative,
double-logarithmically enhanced corrections in the TeV region. These are partly
compensated by real radiation and, moreover, affected by selecting
isospin-noninvariant external states. We investigate the impact of real gauge
boson radiation more quantitatively by considering different restricted final
state configurations. We consider successively a massive abelian gauge theory,
a spontaneously broken SU(2) theory and the electroweak Standard Model. We find
that details of the choice of the phase space cuts, in particular whether a
fraction of collinear and soft radiation is included, have a strong impact on
the relative amount of real and virtual corrections.Comment: 20 pages, 4 figure
Circular holonomy in the Taub-NUT spacetime
Parallel transport around closed circular orbits in the equatorial plane of
the Taub-NUT spacetime is analyzed to reveal the effect of the gravitomagnetic
monopole parameter on circular holonomy transformations. Investigating the
boost/rotation decomposition of the connection 1-form matrix evaluated along
these orbits, one finds a situation that reflects the behavior of the general
orthogonally transitive stationary axisymmetric case and indeed along Killing
trajectories in general.Comment: 9 pages, LaTeX iopart class, no figure
On unitarizability in the case of classical p-adic groups
In the introduction of this paper we discuss a possible approach to the
unitarizability problem for classical p-adic groups. In this paper we give some
very limited support that such approach is not without chance. In a forthcoming
paper we shall give additional evidence in generalized cuspidal rank (up to)
three.Comment: This paper is a merged and revised version of ealier preprints
arXiv:1701.07658 and arXiv:1701.07662. The paper is going to appear in the
Proceedings of the Simons Symposium on Geometric Aspects of the Trace Formul
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