Quasi-Whittaker modules for the Schr\"odinger algebra

In this paper, we construct a new class of modules for the Schr\"{o}dinger algebra \mS, called quasi-Whittaker module. Different from \cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra \mH. We prove that, for a simple \mS-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite \mH-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in U(\mS) and their quasi-Whittaker vectors. Finally, we characterize arbitrary quasi-Whittaker modules.Comment: 17 page

Module structure on U(H) for basic Lie superalgebras

We study the category M consisting of modules whose restriction to U(H) is free of rank 1 for the basic Lie superalgebras. We show that M is not empty only for the Lie superalgebra B(0, n) = osp(1|2n). We classify the isomorphism classes of objects in M for osp(1|2n) and determine their irreducibility. This leads to a lot of new modules over osp(1|2n).ArticleToyama mathematical journal, vol.37, 2015, Page 55-72departmental bulletin pape

Correlated two-photon imaging with true thermal light

We report the first experimental demonstration of two-photon correlated imaging with true thermal light from a hollow cathode lamp. The coherence time of the source is much shorter than that of previous experiments using random scattered light from a laser. A two-pinhole mask was used as object, and the corresponding thin lens equation was well satisfied. Since thermal light sources are easier to obtain and measure than entangled light it is conceivable that they may be used in special imaging applications.Comment: 3 pages, 5 figures, accepted by Optics Letter