Shintani functions, real spherical manifolds, and symmetry breaking operators

For a pair of reductive groups $G \supset G'$, we prove a geometric criterion for the space $Sh(\lambda, \nu)$ of Shintani functions to be finite-dimensional in the Archimedean case. This criterion leads us to a complete classification of the symmetric pairs $(G,G')$ having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of $dim Sh(\lambda, \nu)$ is also obtained. Furthermore, we prove that symmetry breaking operators of the restriction of smooth admissible representations yield Shintani functions of moderate growth, of which the dimension is determined for $(G, G') = (O(n+1,1), O(n,1))$.Comment: to appear in Progress in Mathematics, Birkhause

Generic singularities of symplectic and quasi-symplectic immersions

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.Comment: 12 page

Fermi Surface Study of Quasi-Two-Dimensional Organic Conductors by Magnetooptical Measurements

Magnetooptical measurements of several quasi-two-dimensional (q2D) organic conductors, which have simple Fermi surface structure, have been performed by using a cavity perturbation technique. Despite of the simple Fermi surface structure, magnetooptical resonance results show a dramatic difference for each sample. Cyclotron resonances (CR) were observed for q-(BEDT-TTF)2I3 and (BEDT-TTF)3Br(pBIB), while periodic orbit resonances (POR) were observed for (BEDT-TTF)2Br(DIA) and (BEDT-TTF)3Cl(DFBIB). The selection of the resonance seems to correspond with the skin depth for each sample. The effective mass of POR seems to have a mass enhancement due to the many-body effect, while effective mass of CR is independent of the strength of the electron-electron interaction. The scattering time deduced from each resonance's linewidth will be also presented.Comment: 10 pages, 8 figures, to be published to J. Phys. Soc. Jpn Vol.72 No.1 (accepted

Electric Dipole Moments of Neutron-Odd Nuclei

The electric dipole moments (EDMs) of neutron-odd nuclei with even protons are systematically evaluated. We first derive the relation between the EDM and the magnetic moment operators by making use of the core polarization scheme. This relation enables us to calculate the EDM of neutron-odd nuclei without any free parameters. From this calculation, one may find the best atomic system suitable for future EDM experiments.Comment: 4 page

How are Forbush decreases related to interplanetary magnetic field enhancements ?

Aims. Forbush decrease (FD) is a transient decrease followed by a gradual recovery in the observed galactic cosmic ray intensity. We seek to understand the relationship between the FDs and near-Earth interplanetary magnetic field (IMF) enhancements associated with solar coronal mass ejections (CMEs). Methods. We use muon data at cutoff rigidities ranging from 14 to 24 GV from the GRAPES-3 tracking muon telescope to identify FD events. We select those FD events that have a reasonably clean profile, and magnitude > 0.25%. We use IMF data from ACE/WIND spacecrafts. We look for correlations between the FD profile and that of the one hour averaged IMF. We ask if the diffusion of high energy protons into the large scale magnetic field is the cause of the lag observed between the FD and the IMF. Results. The enhancement of the IMF associated with FDs occurs mainly in the shock-sheath region, and the turbulence level in the magnetic field is also enhanced in this region. The observed FD profiles look remarkably similar to the IMF enhancement profiles. The FDs typically lag the IMF enhancement by a few hours. The lag corresponds to the time taken by high energy protons to diffuse into the magnetic field enhancement via cross-field diffusion. Conclusions. Our findings show that high rigidity FDs associated with CMEs are caused primarily by the cumulative diffusion of protons across the magnetic field enhancement in the turbulent sheath region between the shock and the CME.Comment: accepted in A&