382 research outputs found
Dunkl operators and a family of realizations of osp(1|2)
In this paper, a family of radial deformations of the realization of the Lie
superalgebra osp(1|2) in the theory of Dunkl operators is obtained. This leads
to a Dirac operator depending on 3 parameters. Several function theoretical
aspects of this operator are studied, such as the associated measure, the
related Laguerre polynomials and the related Fourier transform. For special
values of the parameters, it is possible to construct the kernel of the Fourier
transform explicitly, as well as the related intertwining operator.Comment: 28 pages, some small changes, accepted in Trans. Amer. Math. So
Curved Casimir Operators and the BGG Machinery
We prove that the Casimir operator acting on sections of a homogeneous vector bundle over a generalized flag manifold naturally extends to an invariant differential operator on arbitrary parabolic geometries. We study some properties of the resulting invariant operators and compute their action on various special types of natural bundles. As a first application, we give a very general construction of splitting operators for parabolic geometries. Then we discuss the curved Casimir operators on differential forms with values in a tractor bundle, which nicely relates to the machinery of BGG sequences. This also gives a nice interpretation of the resolution of a finite dimensional representation by (spaces of smooth vectors in) principal series representations provided by a BGG sequence
An analysis of interplanetary solar radio emissions associated with a coronal mass ejection
Coronal mass ejections (CMEs) are large-scale eruptions of magnetized plasma
that may cause severe geomagnetic storms if Earth-directed. Here we report a
rare instance with comprehensive in situ and remote sensing observa- tions of a
CME combining white-light, radio, and plasma measurements from four different
vantage points. For the first time, we have successfully applied a radio
direction-finding technique to an interplanetary type II burst detected by two
identical widely separated radio receivers. The derived locations of the type
II and type III bursts are in general agreement with the white light CME recon-
struction. We find that the radio emission arises from the flanks of the CME,
and are most likely associated with the CME-driven shock. Our work demon-
strates the complementarity between radio triangulation and 3D reconstruction
techniques for space weather applications
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