6,547 research outputs found

    Shintani functions, real spherical manifolds, and symmetry breaking operators

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    For a pair of reductive groups GGG \supset G', we prove a geometric criterion for the space Sh(λ,ν)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)(G,G') having finite-dimensional Shintani spaces. A geometric criterion for uniform boundedness of dimSh(λ,ν)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))(G, G') = (O(n+1,1), O(n,1)).Comment: to appear in Progress in Mathematics, Birkhause

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

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    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

    Generic singularities of symplectic and quasi-symplectic immersions

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    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
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